Integrating set pair analysis and social network analysis to explore the distribution pattern and return flow mechanism of floating population: A case study of Heilongjiang Province, China

Integrating set pair analysis and social network analysis to explore the distribution pattern and return flow mechanism of floating population: A case study of Heilongjiang Province, China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Integrating set pair analysis and social network analysis to explore the distribution pattern and return flow mechanism of floating population: A case study of Heilongjiang Province, China Jiyun Bai, Chengyu Yang, Xinyue Jin, Ying cao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8877013/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Under the background of accelerating the development of new quality productivity in China, population mobility, as a key factor, has become increasingly prominent in its spatial reorganization mechanism and regional differential effect. Based on Baidu migration big data and statistical yearbook data, this paper constructs a set pair-social network analysis method, optimizes social network data, enhances network characteristics, and comprehensively describes the network pattern of inter-provincial population mobility. Taking Heilongjiang Province of China as an example, this paper deeply analyzes the spatio-temporal evolution characteristics of population mobility and the driving mechanism of return flow of new quality productivity. The results show that the national population mobility network shows significant small-world characteristics and "core-edge" structure, and the regions with higher levels of new quality productivity occupy the hub position in the network. Heilongjiang Province is on the edge of the population flow network, with continuous outflow of population and highly uneven spatial distribution. The regression analysis shows that the new quality productivity has a significant negative impact on the overall population net flow in Heilongjiang Province, reflecting the mismatch between the development model of new quality productivity with technology intensive and low employment elasticity and the structure of local labor force. However, in cities with low population density, the new quality productivity has a significant role in promoting population return. The results show that the new quality productivity does not naturally have a population attraction effect, and its population effect highly depends on the matching degree between regional industry carrying capacity and population structure. This paper provides a new theoretical perspective and empirical basis for understanding the population mobility mechanism in developing regions and formulating differentiated population return policies. new quality productivity Set-pair-social network analysis Net population flow Return flow drive Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1 Introduction Population is the core resource of a city, which can not only promote the development of urban economy, but also promote the prosperity of social culture, which plays a crucial role in the sustainable development of a city. The migration and mobility of population within a certain spatial range can, to some extent, promote the re-aggregation and diffusion of socio-economic elements. From a geographical perspective, the scale of population mobility has become a comprehensive reflection of many economic and social phenomena, such as unbalanced regional economic development and urban-rural dual structure (Pan., 2019). China has a large population that spreads information, capital, and other resources between cities, which not only contributes to the geographical distribution of our population, but also influences our policies, society, and economy. The spatial distribution of population is an important factor to measure the relationship between human development and regional development mode, and the excessive concentration and dispersion of population are the constraints of sustainable urban development (Wang., 2023). Excessive population concentration is accompanied by resource depletion and excess environmental sustainability. Overdispersion of population may lead to unequal regional development along with social resources such as infrastructure, exacerbate the unbalanced development of regions in the process of population mobility, and lead to a cumulative causal cycle of unequal population distribution (Ye., 2020). In 2023, General Secretary Xi Jinping first put forward the concept of "new quality productivity" during his local inspection.Under the background of the era when new quality productivity has become the core of promoting high-quality development, population, as the most dynamic strategic resource of a city, is deeply integrated with industrial upgrading and scientific and technological innovation, and has become the key factor to promote urban economic and social development. The development of new quality productive forces cannot be separated from the agglomeration and flow of high-quality and highly skilled talents. Talents are not only the main force of technological innovation, but also the promoter of industrial change, which can promote the optimization of urban economic structure and inject strong impetus into urban sustainable development through concept renewal, technology diffusion and knowledge dissemination (Kuang., 2025). At present, China is making every effort to promote Chinese-style modernization, and new quality productivity is the core support to achieve this grand goal (Li., 2025). The 20th Report of the Communist Party of China emphasizes the "modernization with a huge population scale", which provides a broad human resource base for the development of new quality productive forces. Under the wave of rapid development of new quality productivity, the spatial flow of population in China has accelerated, reshaping the pattern of population distribution. Taking Heilongjiang Province in northeast China as an example, in 2020, the large economic development gap between Heilongjiang Province and other regions accelerated the population outflow. The population of Heilongjiang Province was once in the stage of negative growth. According to the data of the seventh census, the total population of Heilongjiang Province was 31.65 million, and compared with the sixth census, the total population of Heilongjiang Province decreased by 6.4 million. The average annual growth rate was − 1.83 percent, and the rate of negative growth was significantly faster than the national average. Against the background of the gradual decline of the total population, the related problems such as the slowdown of urbanization, the acceleration of population aging and the decline of the birth rate have become increasingly prominent.​ Retain the existing population (Wang., 2021). Therefore, under the dual background of rapid population flow and vigorous development of new qualitative productivity, this paper considers the requirements of Chinese-style modernization development and the strategy of high-quality population development, proposes the set-pair social network analysis method, deeply studies the pattern of national social network, as well as the spatio-temporal characteristics of population flow in Heilongjiang Province, and explores the impact of new qualitative productivity on population flow. To find the population return strategy that meets the development needs of new quality productivity, and provide feasible countermeasures and suggestions for optimizing population structure, cultivating new quality productivity, and realizing the high-quality development of regional economy and society. 2 Literature review Scholars have carried out systematic research on the spatial distribution of migrant population and formed rich empirical results. Based on the 1982–1987 census data, Zhang Shan-yu found that China's population migration showed a certain spatial shift, and the migration pattern did not continue the movement from dense areas to sparse areas (Zhang., 1990). Yang Yunyan further revealed that under the effect of the acceleration of urbanization and the difference in regional economic development, the direction of population flow has been fundamentally restructured from the northwest inland to the southeast coast, forming a transformation path from "extension expansion to connotation agglomeration" (Yang., 1993). In the era of network analysis, Khanna et al. described the use of complex network analysis methods to study the impact of COVID-19 on India's migrant population (Khanna., 2020), Rajan et al. discussed the vulnerability of COVID-19 to India's migrant population (Rajin., 2020), Dale and others have assessed student mobility during COVID-19 in Austria (Dale., 2021). Zhao Ziyu's team proposed to use the scale of net population flow to explore the characteristics of population mobility during the Spring Festival, and by using the transformation centrality and control measurement model, it was concluded that the population mobility during the Spring Festival travel rush was dominated by inter-provincial migration, and the urban functional status showed hierarchical distribution in the network (Zhao., 2017). In recent years, the research has shown a trend of multi-scale deepening: Liu Xiaoyang's team constructed a spatial-temporal correlation network model of cities around Bohai Sea based on the frequency data of high-speed trains, and found that both regional connection strength and network efficiency had been significantly improved (Liu., 2023). Relying on Tencent migration big data, Zhang Weili's team used complex network analysis to reveal that China's 11 major urban agglomerations show the characteristics of small world inside, and the urban hierarchy shows the evolution characteristics of "pyramid-shaped" hierarchical organization structure (Zhang., 2023). Through scale transformation and method innovation, these studies systematically analyzed the evolution mechanism of the spatial distribution of migrant population. In terms of the interaction mechanism between the development of new qualitative productivity and population mobility, scholars pointed out that the new qualitative productivity has a significant impact on the decision of population mobility. The development of new quality productivity requires the innovation and optimization of production factors, which promotes the changes of population in entrepreneurial tendency, employment choice, skill upgrading demand and other aspects (Cai., 2025;Zhu., 2024). For example, the emergence of new industries and technologies creates a large number of new jobs and attracts the migrant population with relevant skills, while the traditional mobility model cannot meet the requirements of "new quality" of new productivity and promote the optimization and adjustment of labor mobility pattern. From the perspective of regional differences, unbalanced regional development is still a prominent problem restricting China's high-quality development (Peng., 2024). At present, China has the problem of spatial mismatch of urban talents, for example, the "selection" effect of big cities leads to insufficient agglomeration of highly skilled talents, and the "homogeneous" "talent war" leads to insufficient agglomeration of diversified talents, which affects the balanced development of new quality productivity in space. For different rural and urban areas, the research also has its own emphasis. In rural areas, the migration of rural population to the cities and the return of some population to the countryside have an impact on the development of rural new quality productivity. In cities, the development of new quality productivity affects the scale, structure and trend of urban population mobility, and cities also need to optimize population structure and enhance urban competitiveness and sustainable development ability by improving new quality productivity. 3. Data sources, research methods and variable selection 3.1 Data sources The data set of the study comes from an open data source, and the data used is mainly from the big data of migration provided by Baidu, and also refers to the data of China Statistical Yearbook. Migration big data has the characteristics of real-time, objective and comprehensive, and its data accuracy can be traced back to the individual level, so as to compensate for the one-sidedness of the data. This study takes 31 administrative units above the provincial level (referred to as provinces) in China as the research objects, and Taiwan, Hong Kong and Macao Special Administrative Region are not included due to the lack of data availability. 3.2 Set pair - social network analysis 3.2.1 Set pair analysis Set pair analysis (Zhao., 1995) is a systematic theory and method that uses relation number to deal with uncertainty caused by fuzzy, random, intermediary and incomplete information. It gives objective recognition to all kinds of uncertainty existing objectively, and makes dialectical analysis and mathematical treatment of uncertainty and certainty as a system of identical and different anti-system. It comprehensively describes the relationship between two different things, which is of great significance to the in-depth research and development of system science. Given two sets A and B, and suppose that these two sets form the set pair H=(A,B) , under a specific problem background (let be W ), the characteristics of the set pair H are analyzed, and N features are obtained, where: In A set pair H , if there are S features common to sets A and B , sets A and B are opposite on P features, and on the remaining F = N − S − P features are neither opposite to each other nor common to both sets, then: a = S/N is the same degree of these two sets under the problem W , referred to as the same degree; b = F/N is the dissimilarity degree of these two sets under problem W , which is called dissimilarity degree. c = P/N is the opposite degree of these two sets under problem W , referred to as opposite degree, then: µ = a + bi+cj (1) It is called the connection degree of two sets A , B , and i , j is the mark, which is used to distinguish the same degree. Where a , b and c satisfy the normalization condition a + b+c = 1 . The three parameters a , b and c in the connection number reflect the same, different and anti-connection degree of the two sets, and the difference of their sizes reflects a certain connection trend of the two sets under the specified problem background, which is defined as the connection potential: When c ≠ 0 in connection degree µ = a + bi+cj , the ratio a/c of the same degree a and the opposite degree c is the connection potential of the two sets under the specified problem background, which can be written as follows. shi (H) = a/c (2) When c = 0 in connection degree µ = a + bi+cj , the ratio of the same degree a to the difference degree b is the connection potential of the two sets in the specified problem context, which can be written as follows. shi (H) = a/b (3) The connection potential energy avoids the imbalance of the same, different and contrary data system caused by different levels and different times. Therefore, this paper uses the connection potential index to describe the intensity of population flow and reflect the spatial relationship of population flow between two provinces. It is used as the initial value of the input matrix of social network analysis, which lays a foundation for the subsequent use of social network analysis. 3.2.2 Social Network Analysis Social network analysis method is a quantitative research tool developed by sociologists based on mathematical methods and graph theory. This method systematically analyzes the structural characteristics and interaction rules of the relationship network between social entities by constructing a node and connection model. In this paper, the method of social network analysis will be used to construct the spatial relationship model of population flow with cities as nodes and inter-city population flow as links, to deeply explore the structural characteristics and hierarchical relationship of population flow network between different regions in the development process of new qualitative productivity, and to reveal the internal relationship between population flow and the development of new qualitative productivity. Commonly used network analysis metrics include: (1) degrees Degree can describe the state of interconnection between nodes, thus reflecting the evolution characteristics of the network (Neal., 2011). In the directed network, it is divided into two concepts: in-degree and out-degree. In this paper, only in-degree is considered in the study of backflow population. There are different in-degrees in the mobility network of urban nodes, which represent the attractiveness and radiation force of the city under a certain measurement standard. The calculation formula is as follows: $$\:{\text{W}}_{\text{m}\text{i}}\text{=}\sum\:_{\text{k}\text{=1}}^{\text{n}}{\text{R}}_{\text{mk}\text{j}}$$ 4 Here, \(\:{\text{W}}_{\text{m}\text{i}}\) represents the total indegree value of city \(\:\text{m}\) in the study period, and R mkj represents the value of the path that generates inflow relationship between other cities and city \(\:\text{m}\) in day \(\:\text{j}\) . $$\:{\text{W}}_{\text{mo}}\text{=}\sum\:_{\text{k}\text{=1}}^{\text{n}}{\text{R}}_{\text{mkj}}$$ 5 Here, \(\:{\text{W}}_{\text{mo}}\) represents the total outdegree value of city \(\:\text{m}\) in the study period, and \(\:{\text{R}}_{\text{mkj}}\) represents the value of the path that city \(\:\text{m}\) generates outflow relationships with other cities in day \(\:\text{j}\) . (2) Betweenness centrality Betweenness centrality reflects the influence and control of a city when it interacts with other cities in the population flow network. Nodes with higher betweenness centrality are more important in the network and have stronger control ability over other nodes, which can be calculated as follows: $$\:{\text{e}}_{\text{m}}\text{=}\sum\:_{\text{ν}\text{≠}\text{m}}\frac{\text{n}\text{(}\text{u}\text{,}\text{v}\text{|}\text{m}\text{)}}{\text{n}\text{(}\text{u}\text{,}\text{v}\text{)}}$$ 6 Where \(\:\text{n}\) ( \(\:\text{u}\) , \(\:\text{v}\) ) is the number of shortest paths between node \(\:\text{u}\) and v , and n( \(\:\text{u}\) , \(\:\text{v}\) | \(\:\text{m}\) ) is the number of shortest paths between \(\:\text{u}\) and \(\:\text{v}\) connected by node \(\:\text{m}\) . (3) The clustering coefficient Clustering coefficient reflects the degree of interconnection between nodes (WEI., 2016). When some nodes are particularly closely linked together, a network community can be formed. $$\:{\text{C}}_{\text{i}}\text{=}\frac{\text{2}{\text{B}}_{\text{i}}}{{\text{m}}_{\text{i}}\text{(}{\text{m}}_{\text{i}}\text{−1)}}$$ 7 Where \(\:{C}_{i}\) is the clustering coefficient, \(\:{m}_{i}\) is the number of edges that actually exist between the neighbor nodes of node i , and \(\:{B}_{i}\) is the number of paths between node i and its neighbors. 3.2.3 Set Pair Social Network Analysis and its process Set pair social network analysis combines set pair analysis with social network analysis. It uses set pair analysis to calculate the connection degree between data, so as to obtain the connection potential between data, which is used as the relationship structure value in social networks to calculate network analysis indicators and study network relationships. The set pair analysis method is used to improve the social network analysis, and the network characteristics are enhanced by optimizing the social network data, so as to construct the population mobility network analysis model. In terms of specific measurement, this paper regards the directional characteristics in the data as the uncertain characteristics of the identical, different and contrary relationship in the set pair, and regards the directional uncertainty relationship and the numerical certainty relationship in the population flow data as a system. It studies the value law of the directional characteristics under specific conditions, and quantifies them into the population flow data to comprehensively describe the population flow relationship between two provinces. Traditional social network analysis usually simplifies the relationship between nodes to deterministic directed or weighted connections when dealing with the problem of population flow, and its essential assumption is that the strength and direction of the flow relationship are statistically stable and fully observable. However, in the study of population mobility based on migration big data, the relationship between nodes often has the characteristics of directional asymmetry, intensity fluctuation and statistical incompleteness at the same time. It is easy to ignore the implied intermediary states and fuzzy relationships in the process of population mobility simply by describing the flow scale or weighting matrix, which weakens the expression ability of network structure features. The specific process is as follows: (1) Determine the set pair according to the research content, and select the characteristics of the set pair data. The research content of this paper is the population flow between provinces, so the two provinces are combined into a set pair, and the direction characteristics of the population flow data between provinces are selected. (2) The characteristics of the data are summarized and the attributes are divided. In this study, the directional characteristics of four population flow data for each province are summarized as shown in Fig. 1 below, and the attributes are divided and defined as the same degree a and the difference degree b. (3) According to the characteristics of same degree and difference degree determined above, calculate the connection degree according to Formula (1). In this study, each province is defined as a set, and any two provinces form a set pair H . Considering the directional characteristics of population flow data, the characteristics are summarized and divided into attributes. The a is the same characteristics shared by the two provinces, b is the characteristics that are neither the same nor different between the two provinces, and c is 0 because there are no different characteristics. It is combined into the same, different and contrary system to calculate the connection number µ , quantify the data characteristics, and comprehensively describe the connection between two provinces. (4) Calculate the contact potential according to Eq. (3), and use the contact potential as social network data to construct the correlation matrix of population mobility. The connection potential can avoid the characteristics of data imbalance caused by different levels and different times. Therefore, this paper uses the connection potential index to describe the intensity of population flow and reflect the spatial relationship of population flow between two provinces. (5) The calculated contact potentials are used as social network data, and the spatial relationship matrix represents the flow characteristics of the population in a day. (6) The calculated initial matrix of spatial relationship is binarized and used as the input matrix of social network analysis, and the clustering coefficient and network centrality parameters of population flow between provinces are obtained through UCINET. At the same time, the UCINET input matrix is imported into the visualization tool ArcGIS. A specific graphical representation of the results of the population mobility network can be directly observed. 3.3 Measurement of hierarchical characteristics of population mobility network 3.3.1 Population offset growth The shift-share method was proposed by Creamerl earlier and has been widely used in the study of regional economic growth and population pattern evolution. Among them, "sharing" refers to the amount of growth obtained according to the regional growth rate, and "offset" refers to the difference between absolute growth and shared growth. The formula is as follows: $$\:\text{s}\text{h}\text{if}{\text{t}}_{\text{i}}\text{=}\text{absg}{\text{r}}_{\text{i}}\text{−}\text{s}\text{h}\text{ar}{\text{e}}_{\text{i}}$$ $$\:\text{=}\text{po}{\text{p}}_{\text{i}}\text{(}{\text{t}}_{\text{1}}\text{)−}\frac{\sum\:_{\text{i}\text{=1}}^{\text{n}}\text{p}\text{o}{\text{p}}_{\text{i}}\text{(}{\text{t}}_{\text{i}}\text{)}}{\sum\:_{\text{i}\text{=1}}^{\text{n}}\text{pop}\text{(}{\text{t}}_{\text{0}}\text{)}}\text{×}\text{po}{\text{p}}_{\text{i}}\text{(}{\text{t}}_{\text{0}}\text{)}$$ 8 Where, \(\:shif{t}_{i}\) , \(\:absg{r}_{i}\) and \(\:shar{e}_{i}\) respectively represent the offset growth, absolute growth and shared growth of population of city i in the time period of ( \(\:{t}_{0}\) , \(\:{t}_{1}\) ), \(\:po{p}_{i}\) is the total population of the city, n denotes the number of cities. Positive offset growth indicates a strong population agglomeration ability, and vice versa a weak population agglomeration ability. 3.3.2 Gini coefficient Gini coefficient(Liu., 2016) first appeared in the field of income distribution difference research, and subsequent studies have extended it to quantitative analysis of the characteristics of unbalanced spatial distribution of population. In this study, the method is introduced into the evaluation of the equilibrium of the spatial distribution of the outflow population. By calculating the distribution difference of the outflow scale between different regions, the spatial agglomeration degree and dynamic change characteristics of the population flow are objectively measured. The calculation formula is as follows: $$\:\text{G}\text{=1−}\frac{\text{1}}{\text{n}}\text{(2}\sum\:_{\text{i}\text{=1}}^{\text{n}\text{−1}}{\text{w}}_{\text{i}}\text{+1}\text{)}$$ 9 Where, \(\:\text{G}\) is Gini coefficient, and the value is between 0 and 1. The larger the value is, the more concentrated the spatial distribution of the outflow population is.On the contrary, the more dispersed it is.; \(\:{\text{w}}_{\text{i}}\) represents the proportion of the population flowing into region i to the total outflow, and n represents the number of regions. 3.4 New mass gravity-population mobility response model 3.4.1 Baseline regression models On the basis of controlling regional heterogeneity and time effect, this paper accurately identifies the influence of new quality productivity on population mobility. Based on the data of population mobility and new quality productivity development in Heilongjiang Province, this paper establishes a bilateral fixed effect regression model to systematically test the driving effect of the two from the measurement level, so as to realize the mechanism expansion and deepening of the above spatial pattern analysis results. The reflow strategy is put forward. $$\:{\text{NPI}}_{\text{it}}\text{=}{\text{a}}_{\text{0}}\text{+}{\text{a}}_{\text{1}}{\text{NQP}}_{\text{it}}\text{+}{\text{a}}_{\text{2}}\text{ln}{\text{C}\text{ontrol}}_{\text{it}}\text{+}{\text{μ}}_{\text{t}}\text{+}{\text{v}}_{\text{i}}\text{+}{\text{ε}}_{\text{it}}$$ 10 Here, \(\:\text{NPI}\) is the net population flow, \(\:\text{NQP}\) is the level of new quality productivity, \(\:\text{C}\text{ontrol}\) is the set of control variables, i is the city, t is the year, \(\:{\text{μ}}_{\text{t}}\) is the individual fixed effect, \(\:{\text{v}}_{\text{i}}\) is the time fixed effect, and \(\:{\text{ε}}_{\text{it}}\) is a random term. 3.4.2.Variable selection 1. Explained variables In this paper, the net population flow(NPI) is used as the explained variable, which is obtained by using the permanent population-registered population between regions. It can intuitively reflect the population attraction and flow direction of a single city, facilitate the comparison of the change trend of floating population between different cities, and can more accurately reflect the impact of the level of new quality productivity on population flow, and reflect its comprehensive impact on labor inflow and regional development. 2. Core explanatory variables The core explanatory variable of this paper is the development level of new quality productivity(NQP). The new quality productivity evaluation index system is constructed from the three aspects of workers, labor objects and labor materials, as shown in Table 1 . The entropy method is used to synthesize the measures. To understand the level of new quality productivity, we should mainly explore from three aspects: workers, labor objects and labor materials. As the core driving force, workers are high-quality talents with advanced technology and innovation ability. Through research and development, knowledge application and model innovation, they can promote the high-quality development of new productive forces. The labor object is the material foundation, the new labor object expands the production boundary, the high quality labor object can improve the product quality, and promote the development of green industry. Labor materials are technical support, and advanced production tools and equipment support technological innovation, reduce costs, optimize production processes, promote industrial integration, and give birth to new forms of business. The three are interconnected and synergistic, promoting productivity to break through the traditional development path, and building a new quality productivity system with innovation as the core, high-tech and high-quality characteristics. Table 1 Measurement Index System of New Productive Forces First level indicator second-level indicators Indicator Meaning Laborer Supply and quality of human capital Number of regular institutions of higher learning Number of employees in strategic emerging industries Average wage of employees on the job Main output of innovation Number of inventions filed in the current year Number of utility models applied in the current year Number of green inventions filed that year Number of green utility models applied in that year labor object Data element resources Level of utilization of data elements Whether there is a data trading platform Carbon trading/energy trading volume Ecological environment resources Harmless disposal rate of household garbage Investment in environmental pollution control labor material Digital infrastructure Number of Internet broadband access users Total amount of telecommunications services Intelligent technical equipment Robot mounting density Number of AI enterprises Innovation input guarantee The proportion of science expenditure in local fiscal expenditure 3. Control variables The control variables and measurement methods of this paper are as follows: (1) Economic development level (EDL), represented by per capita regional product; (2) Financial development level (FDL), the balance of deposits and loans of financial institutions at the end of the year/regional GDP; (3) The level of opening to the outside world (OPEN), which is obtained by the amount of foreign capital actually utilized/GDP of the region; (4) The degree of government intervention (GOV), the expenditure in the general budget of local finance/regional GDP; (5) Industrial structure (IND), the value added of the tertiary industry/GDP. In this paper, the log form of continuous control variables is taken to reduce skewness and mitigate the impact of extreme values. 4. Descriptive statistics of data In order to eliminate the dimensional differences, the explained variables are standardized by range, and the descriptive statistics are shown in Table 2 below: Table 2 Descriptive Statistics of Variables Variables Mean Mtandard deviation Minimum Maximum NPI 0.472 0.196 0 1 NQP 0.031 0.057 0.003 0.239 EDL 10.429 0.478 9.434 11.905 FDL 2.678 1.066 0.588 5.586 OPEN 0.002 0.002 0 0.008 GOV 0.289 0.131 0.044 0.675 IND 0.402 0.096 0.144 0.677 4 Empirical analysis 4.1 Analysis of spatio-temporal evolution of provincial population mobility based on set pair association network 4.1.1 Degree value analysis Based on the degree value analysis of the spatial correlation network structure of China's inter-provincial population mobility, the network structure is stable and the index fluctuation is small during the study period, so only the data in 2023 are selected for analysis. Ucinet software is used to calculate the degree value of population mobility network in 31 provincial-level administrative regions, and it is found that the degree centrality is within the interval [0,15], and the differences in spatial connections between provinces lead to unbalanced population mobility, as shown in Table 3 . Guangdong province, Jiangsu Province and other top ten provinces in terms of point access degree, whose degree values are higher than the national average, play a key role in the population mobility network and become the core of network cohesion and integration. Relying on the advantages of economy, geography, resources and transportation, these provinces show significant siphon effect, which not only has a strong attraction, but also forms an aggregation effect. Table 2 Characteristics of Entry and Exit Provinces Point out degree Point in degree Guangdong Province 15 15 Jiangsu Province 14 15 City of Tianjin 14 14 Hubei Province 12 13 Zhejiang Province 12 12 Shanghai City 11 13 Sichuan Province 12 11 Hunan Province 11 12 Beijing City 12 10 Shandong Province 11 10 4.1.2 Betweenness centrality analysis The betweinness centrality reflects the transportation capacity and aggregation capacity of each province in the population mobility network. It can be seen from Fig. 2 that the nodes with high centrality in the middle of population mobility are mainly located in the eastern region, with them as the center and scattered around, showing a core-periphery structure, and the centrality and total degree of provincial administrative regions are positively correlated. The greater the intermediate centrality is, the more the province is in the core position, and it has the control advantage to control the communication of all other points, which can play the role of a bridge connecting all provinces. It can be seen from the figure that the intermediate centrality of Beijing, Tianjin and Shanghai is relatively large, and the centrality of Shanghai is the first in the three periods. It can be seen that regions with slow development of new quality productivity, such as Heilongjiang Province, are at the edge of the network, with little connection effect and unable to control the interaction of other points. 4.1.3 Cluster coefficient analysis As a key indicator to measure the clustering characteristics of network nodes, the clustering coefficient reflects the local density of connections between nodes. The research shows that the average clustering coefficient of population mobility network in provincial administrative areas in China in 2019, 2021 and 2023 is over 0.5, higher than that of random network, and the network path length is stable at about 2.0, showing the typical characteristics of small world network. This feature of "high cluster-short path" not only means that the population mobility network has efficient information transmission efficiency, but also provides a structural basis for the cross-regional mobility and collaborative innovation of new quality productivity factors. The short path feature promotes the rapid diffusion of innovation elements and the balanced development of new quality productivity among regions. Community structure theory, which emphasizes the stable association and dynamic evolution of elements within a system, has been widely used in the study of complex networks in recent years. Through the modular cluster analysis of the inter-provincial population mobility network by Gephi software, it is found that the country can be divided into four communities: northeast - North China, Northwest China, East - South China, and southwest - South China, as shown in Fig. 3 . Provinces within the same community are closely connected in space, which reflects the restriction of geospatial effect on population mobility. From the perspective of new quality productivity, this community structure provides opportunities for regional coordinated development. For example, the northeast and North China communities where the three northeastern provinces are located are spatially adjacent to each other, which is conducive to the construction of a collaborative development circle of new quality productivity and the acceleration of technological innovation and achievement transformation through industrial complementarity and resource sharing. The strengthening of the trend of population mobility across large-scale geographical space will further promote the optimal allocation of new qualitative productivity factors, promote Heilongjiang and other old industrial bases to use external innovation resources, accelerate the transformation and upgrading of traditional industries, improve the allocation of social resources, and inject new momentum into the cultivation and development of new qualitative productivity. 4.2 Calculation of hierarchical characteristics of population mobility network in Heilongjiang Province 4.2.1 Situation and stage characteristics of population mobility The dynamic evolution of the spatial pattern of migrant population is essentially the mapping result of the heterogeneity of regional growth at different administrative levels in the spatial dimension. Therefore, in order to deeply analyze the dynamic evolution mechanism of the spatial distribution of migrant population, it is necessary to start from the spatial expression of the growth difference of multi-scale regional migrant population, quantitatively analyze the spatial differentiation characteristics of the growth intensity among regions, and reveal the internal driving factors of the spatial pattern of population migration. The dynamic evolution of the spatial distribution pattern of regional floating population is caused by the offset growth of each region and its subordinate provinces. Based on this, to explore the evolution trajectory of the spatial pattern of migrant population, it is necessary to start from the migration growth characteristics of the migrant population in each region and its subordinate provinces. And the specific performance of the growth rate. The spatial distribution of the migration growth of China's migrant population from 2013 to 2022 is obtained through calculation, and the specific data are shown in Table 4 . Based on these data, this paper sorts out the main clues of the evolution of the spatial pattern of China's floating population, explores the relationship between the migration growth rate of Heilongjiang Province and other provinces, and reveals its internal rules and characteristics. Table 4 − 1 Migration and Growth of Floating Population in Various Regions Eastern region Central region Western region Northeast region Beijing 266.25 Henan 98.04 Inner Mongolia 55.39 Liaoning 90.59 Tianjin 6.57 Hubei -64.84 Yunnan -7.05 Ji Lin -123.96 Hebei -15.61 Hunan -29.64 Sichuan -89.32 Heilongjiang -26.10 Shandong 35.026 Jiangxi -74.65 Guizhou -182.02 Shanghai 112.5 Anhui 198.70 Chongqing 6.72 Jiangsu 37.23 Shanxi 126.41 Shaanxi -167.24 Zhejiang 244.57 Gansu -98.07 Fujian -26.53 Qinghai -10.29 Guangdong -140.68 Ningxia -9.57 Hainan -57.19 Xinjiang -5.79 Guangxi -119.58 Xizang -6.28 Total amount 462.14 Total amount 254.02 Total amount -636.05 Total amount -59.47 Since 2013, the migration growth of migrant population in all provinces in China has maintained a stable situation in terms of overall scale and growth intensity. The data show that the total number of migrant population in China increased by 92,472,200 during this period, indicating that the growth of migrant population during this period showed a significant expansion trend due to the factor mobility vitality brought by the development of new quality productivity. From the regional dimension, although the overall evolution trend of the migration growth of migrant population in the four regions has a certain synchronicity, there are obvious spatial differences in the growth intensity under the influence of the spatial heterogeneity of the development level of the new quality productivity, which reflects the regional differentiation of the traction and remodeling effect of the new quality productivity on population migration. The migration growth of floating population in Heilongjiang is − 26.10, showing a trend of population outflow. From the perspective of new quality productivity, this is related to the development level of regional new quality productivity. If the cultivation of emerging industries and the agglomeration of innovation factors are insufficient, the upgrading of traditional industries will be slow, and the attraction of employment and development space to the population will weaken. At the same time, it is also necessary to pay attention to its distribution potential in the fields of new quality productivity such as digitalization of ice and snow economy and intelligence of energy industry. If high-quality employment and development opportunities can be created by developing new industries such as smart agriculture and green energy, it is expected to optimize the pattern of population mobility and realize the two-way empowerment of population and new quality productivity development. The spatial network diagram drawn by ArcGIS shows that in Fig. 4 , the population flow in Heilongjiang Province in 2019, 2021 and 2023 shows a pattern of "dense in the east and sparse in the west," which has both the characteristics of proximity and jump, and is closely related to the development of new quality productivity. As a core factor, population's mobility pattern affects innovation, factor allocation and industrial upgrading, and accelerates the spread of knowledge and technology. The population flow between Heilongjiang and Liaoning, Beijing, Jilin and other neighboring regions promotes the sharing of innovative resources and the absorption of technological ideas, and provides energy for industrial innovation. Due to the close space and complementary industries among neighboring provinces, the synergy between labor and technology can be realized to promote industrial upgrading. Although there is a short-term brain drain in the population flow between Heilongjiang and the eastern provinces, it is conducive to the introduction of experience, technology and capital, the transformation of traditional industries, and at the same time, it gives full play to its own resource advantages to attract innovative factors and promote regional coordinated development. By guiding the reasonable flow of population, optimizing the allocation of resources and deepening regional cooperation, we can fully release its role in promoting the new quality productivity and help Heilongjiang's high-quality economic development. 4.2.2 Gini coefficient measurement of spatial agglomeration characteristics of population out-migration in Heilongjiang Province As the core index to measure the spatial agglomeration effect of industry, the theoretical origin of spatial Gini coefficient can be traced back to the pioneering research of Plane et al in the 1990s. This study introduces the Gini coefficient method into the analysis of the spatial pattern of population mobility, and provides a new idea for analyzing the spatial heterogeneity of population mobility by quantifying the concentration degree of population inflow and outflow between regions. The coefficient ranges from 0 to 1, and the larger the value is, the more significant the regional difference is, the higher the regional concentration of migrant population is, and the more prominent the non-equilibrium characteristics of population distribution are. This index can effectively describe the agglomeration characteristics of the spatial distribution of population.Therefore, this paper uses the Gini coefficient to analyze the regional characteristics of the inter-provincial out-migration of Heilongjiang's population, as shown in Table 5. Table 3 Gini Coefficient Region 2019 2022 2023 Flows into Heilongjiang Province Eastern region 0.7504 0.7517 0.7540 Central Region 0.5963 0.5005 0.5471 Western region 0.6353 0.6006 0.6215 Outflow from Heilongjiang Province Eastern region 0.7296 0.7402 0.7512 Central Region 0.5734 0.5927 0.5976 Western region 0.6522 0.6426 0.6867 Numerically, relying on the agglomeration of new quality productivity in the Pearl River Delta, Yangtze River Delta and Beijing-Tianjin-Hebei urban agglomerations in the eastern region in 2019, the population inflow and outflow in Heilongjiang Province show the characteristics of high spatial agglomeration, and the Gini coefficients are 0.7504 and 0.7296 respectively. Affected by the regional differences of new quality productivity, the distribution of population mobility in the western region is relatively uneven. The development of new quality productivity in the central region is relatively balanced, and the difference in population mobility is small.In 2022,the coordinated and balanced development of new quality productivity in the central and western regions will promote the distribution of population mobility to become more uniform, and the relevant Gini coefficient will decrease significantly, while the agglomeration effect in the eastern region will be further strengthened.In 2023, with the strengthening of regional differentiation and agglomeration effect of the new qualitative productivity, the Gini coefficient of population inflow and outflow in the eastern, central and western regions of Heilongjiang Province shows an upward trend, indicating that the regional heterogeneity of the new qualitative productivity continues to deepen the spatial agglomeration pattern of population flow. Figure 5 intuitively shows the agglomeration differences between the population inflow and outflow regions in 2023. Figure 6 and Fig. 7 respectively show the time series distribution characteristics of population inflow and population outflow, in which the color depth of the color block is positively correlated with the value size. The longitudinal analysis based on the time dimension shows that at the eastern regional level, no matter Heilongjiang province is the place of population inflow or outflow, its Gini coefficient shows an upward trend, indicating that the equilibrium of population distribution in this region has been improved. Specifically, due to the migration of population from a large number of regional provinces to Heilongjiang Province in the eastern region, the spatial distribution balance of the outflow population is significantly enhanced. At the central region level, the Gini coefficient of the population migration from provinces to Heilongjiang Province shows the fluctuation characteristics of falling first and then rising, while the Gini coefficient of the population inflow continues to rise. This change shows that the migration activities of the central provinces lead to the simultaneous increase of the imbalance in the distribution of the outflow and inflow of the population. In the western region, the Gini coefficients of population inflow and outflow show a U-shaped curve characteristic of first decreasing and then increasing, which reflects that the distribution imbalance of urban population migration in this region has experienced a dynamic process of "aggravation-relief-aggravation", and finally shows an overall upward trend. 5. Test and strategy derivation of reflow mechanism driven by new quality productivity In the context of new quality productivity, population return is not a short-term random behavior, but the result of the combined effect of long-term institutional environment, public services and regional development differences.Different regions have significant differences in resource endowment, historical development path and institutional environment,and these unobservable but relatively stable individual characteristics, as well as macroeconomic fluctuations, policy adjustments and other factors,will affect population mobility. Therefore, on the basis of controlling regional heterogeneity and time effect, this paper accurately identifies the net effect of the new quality productivity on population mobility. In this way, the mechanism of the above analysis results of the spatial pattern of migrant population can be expanded and deepened. This model provides a reliable empirical basis for the formulation of subsequent population return policy. 5.1 Benchmark regression results As can be seen from the benchmark regression results, as shown in Table 6 , the new quality productivity has a significantly negative impact on the net population flow of Heilongjiang Province. This result itself has a strong "counterintuitive" feature: referring to the mainstream development economics and population mobility theory, the improvement of productivity usually means the improvement of employment opportunities and the increase of income expectations, thus attracting the population. Considering the realistic background from 2012 to 2022, the improvement of new quality productivity in Heilongjiang Province does not rely on the expansion of population intensive industries, but is more reflected in digitalization, automation, capital deepening and the agglomeration of a few high-end technology sectors. This kind of new-quality productivity has the characteristics of "low employment elasticity" : on the one hand, it compresses the employment space of traditional manufacturing and resource-based industries through technological substitution; On the other hand, highly skilled labor continues to flow efficiently to the well-developed eastern coastal areas, but the new jobs have high requirements on human capital, and the mismatch with the local labor structure is obvious, which ultimately leads to the phenomenon of continuous population outflow despite the good development of productivity. From Model (2), after the control variables are added, the absolute value of NQP coefficient converges but is still significantly negative, indicating that the above mechanism is not explained by other macro factors, but the endogenous result of the new quality productivity itself in the development stage of Heilongjiang Province. It is particularly noteworthy that the industrial structure variable (IND) is also significantly negative, indicating that industrial transformation and upgrading does not form a positive pull on the population in the short term. Furthermore, the variables of education level and financial development do not show a significant impact, which to a certain extent reflects the problem of human capital spillover rather than agglomeration in Heilongjiang Province. At the same time, the insignificant degree of opening up and government intervention also implies that the marginal effect of traditional policy tools in dealing with the impact of new-quality productivity on population mobility is limited. Based on the experience of Heilongjiang Province, the new quality productivity does not naturally have the effect of population attraction, and its impact on population mobility is highly dependent on the matching degree of regional industrial carrying capacity and labor force structure. The result revealed by the benchmark regression is not a simple conclusion that the new quality productivity inhibits the population inflow, but a deeper structural fact. This finding not only provides a new explanatory framework for understanding the population mobility in Heilongjiang Province, but also puts forward an important reflection on the current regional development policy focusing on the new quality productivity. Table 6 Benchmark Regression Results Variables Model (1) Model (2) NQP -4.041 *** (-3.490) -2.037 ** (-2.350) EDL -0.031 (-0.920) FDL -0.038 (-1.600) OPEN -7.836 (-1.360) GOV 0.076 (0.930) IND -0.263 ** (-2.980) Constant term 0.596 *** (16.76) 1.054 ** (2.680) Sample size 156 156 Individual fixed effects YES YES Time fixed effect YES YES R 2 0.212 0.397 5.2 Robustness test 5.2.1 Add lagged term of explained variable Considering the possible inertial characteristics of population flow, this paper introduces the one-period lagged term of net population flow into the benchmark model for robustness test. As shown in Model (1) and Model (2) in Table 7 , the regression coefficients of new quality productivity are significantly negative regardless of whether control variables are added, and the significance level is consistent with the benchmark regression, indicating that the above conclusions are not caused by short-term fluctuations or endogeneity problems. It can be seen that the inhibitory effect of the new quality productivity on the net population flow in Heilongjiang Province has certain continuity and stability, and the population outflow will not be automatically weakened with the passing of time. 5.2.2 Adding control variables After the control variables of economic density(ED) and medical and health care level(MHL) are further introduced on the basis of the benchmark model, although the estimated coefficient of the new quality productivity has changed, the sign and significance have not changed fundamentally. At the same time, the newly added control variables fail to significantly change the direction of population flow, indicating that the continuous outflow of population in Heilongjiang Province is not solely restricted by public services or spatial conditions, but is closely related to the structural development model led by the new quality productivity. In general, the robustness test results are consistent with the previous analysis. Table 7 Results of Robustness tests Variables Model (1), the explained variable is lagged by one period Model (2), the explained variable is lagged by one period Model (3) adds control variables Model (4) adds control variables NQP -5.290 *** (-3.810) -2.809 ** (-2.940) -4.041 *** (-3.490) -1.822 ** (-2.190) EDL -0.045 (-1.140) 0.142 * (2.100) FDL -0.048 (-1.710) -0.044 (-1.580) OPEN -9.136 (-1.340) -6.853 (-1.210) GOV 0.133 (1.400) 0.024 (0.320) IND -0.290 ** (-2.290) -0.345 *** (-3.370) ED -0.204 ** (-2.430) MHL -0.035 (-0.380) Constant term 0.630 *** (14.75) 1.247 ** (2.550) 0.596 *** (16.76) 0.472 (1.240) Sample size 156 156 156 156 Individual fixed effects YES YES YES YES Time fixed effect YES YES YES YES R 2 0.310 0.526 0.212 0.434 5.3 Heterogeneity analysis Population density, as an important indicator to measure the level of urban population agglomeration, reflects the intensity of urban economic activities, the improvement of infrastructure and the supply capacity of public services to a certain extent. Areas with high population density usually have stronger factor agglomeration capacity and more perfect supporting conditions for employment and living, while areas with low population density have constraints such as insufficient attraction to factors. Based on this, this paper groups the samples according to the population density level of cities, and divides the top six cities in population density into the high population density group, and the remaining cities into the low population density group, so as to examine the difference in the effects of the two under different population agglomeration levels, so as to reveal the heterogeneity characteristics behind the average effect.The heterogeneity results are shown in Table 8 . The regression results show that the impact of new quality productivity on net population flow is significantly different in cities with different population density. In cities with high population density, the regression coefficient of the new quality productivity variable is still negative and significant at the 1% significance level, which is consistent with the results of the whole region. In contrast, in cities with low population density, the impact of new quality productivity on net population flow is significantly positive, that is, the development of new quality productivity significantly promotes population return and net population inflow. This result shows that the new quality productivity does not produce a consistent population effect among different cities, and its direction and intensity of influence obviously depend on the population agglomeration level of the city. For cities with high population density, their original population carrying capacity and factor agglomeration level are already at a high state, and the development of new quality productivity is more reflected in technological upgrading and industrial efficiency improvement, with limited marginal absorption capacity for new population, and may even strengthen population outflow by increasing living costs and competitive pressure. For cities with low population density, the development of new quality productivity significantly enhances the ability to attract population by cultivating emerging industries, expanding employment space and improving development expectations, thus effectively promoting population return. Combined with the benchmark regression results, it can be found that the average effect of the new quality productivity on the net population flow in the overall sample is essentially the accumulation of the opposite effects in the above two types of cities. Table 8 Results of Heterogeneity Analysis Variables Model (1) Model (2) NQP -5.646 *** (-7.090) 1.939 ** (2.790) Constant term 0.742 *** (18.46) 0.466 *** (61.460) Sample size 78 78 Individual fixed effects YES YES Time fixed effect YES YES R 2 0.333 0.175 6 Conclusion: New quality productivity-oriented population return strategy From the perspective of new quality productivity, this paper systematically reveals the network pattern and regional differences of population migration in China, and takes Heilongjiang Province as an example to empirically analyze the action mechanism of new quality productivity on population backflow. The results show that the national population mobility network presents a stable small-world structure and significant core-periphery differentiation characteristics, and the regions with higher new quality productivity have stronger ability to attract and control population in the network. In addition, Heilongjiang Province has been at the edge of the population mobility network for a long time, and the characteristics of population outflow are obvious. The measurement results show that the new quality productivity has a negative impact on the overall net population flow in Heilongjiang Province, which is rooted in the mismatch between the development stage of the new quality productivity and the local labor structure. It can be seen that the impact of the new quality productivity on population mobility is obviously situational dependent, and it is necessary to promote the co-evolution of the new quality productivity and high-quality population development by optimizing the industrial carrying capacity, reducing the living cost and improving public services. Based on the above research conclusions, policy recommendations are put forward: 1. Accelerate the development and improvement of the technology market and reduce the risk gap. The large-scale outflow of population in Heilongjiang Province will inevitably lead to the loss of human resources, which directly leads to the lack of technical talent reserves in various industries in the province. The lagging technological competitiveness further weakens the attractiveness of technical talents in Heilongjiang Province, thus forming a vicious circle, which not only seriously restricts the economic development vitality of Heilongjiang Province, but also aggravates the unemployment risk and health risk faced by the returning population. In order to prevent and control health risks, it is necessary to build a more sound social security network system and strengthen the supply of public health services. In terms of unemployment risk, returnees may encounter problems such as poor connection of human resources, insufficient support for entrepreneurship and employment, and disconnection between personal skills and market demand (Cao., 2021). 2. Reduce the material cost of population and increase the utility benefit of returning population. With the steady development of social economy and the significant improvement of people's quality of life, the daily consumption structure is gradually changing to diversified and refined. In addition to meeting the basic living expenses, the family income has become the main source of economic burden for ordinary families (Yang., 2019). In view of this, the government needs to take a series of targeted measures to effectively alleviate the economic pressure of families in this field. The government should focus on improving the quality and coverage of eugenics services. On the one hand, it is necessary to strengthen the construction of professional institutions and talent teams, especially the resource allocation and service capacity of maternal and child health departments of hospitals at all levels, so as to ensure that employees have professional qualifications and skills to meet the growing demand for maternal and child health care. At the same time, at the level of township and community, special maternal and child health service stations should be set up to form a service network covering urban and rural areas, ensure that the policy of eugenic and child-rearing is deeply rooted in the hearts of the people, and provide substantive support such as childcare allowance and tax reduction for highly educated talent families who have two or three children in response to the national policy. In terms of education cost control, the government needs to take a two-pronged approach, not only focusing on the improvement of education quality, but also reducing the economic burden of families. 3. Increase financial support to shorten the income gap According to the explanation of labor economy, most of the reason for the large outflow of population is that the income from outflow is greater than that of Heilongjiang Province.The government needs to adopt proactive strategies through a series of policy tools and measures to guide and encourage talents to return to their hometowns to start businesses, and build a comprehensive and multi-level entrepreneurial support system for returning entrepreneurs, such as optimizing the entrepreneurial environment, providing site support, and simplifying the administrative approval process, so as to effectively alleviate the crowding-out effect that may be caused by the excessive concentration of government-led capital on returning entrepreneurs. Secondly, in terms of capital, the government should set up special entrepreneurial lending institutions and implement differentiated interest rate policies, especially for returning entrepreneurs, and provide more favorable loan conditions to reduce their financing costs and inject strong impetus into entrepreneurial activities. Establish and improve a more active tax policy, improve the individual tax system, reduce the tax burden of high-income groups by adjusting the personal income tax policy ‌, while reducing the amount of tax paid by low-income groups, and narrow the income gap. Declarations Author Contribution Jiyun Bai was responsible for conceptualization, methodology, funding acquisition, and final manuscript review and approval. Chengyu Yang contributed to the original draft preparation, data curation, formal analysis, and visualization. Xinyue Jin participated in methodology development and analysis and interpretation of data. Ying Cao contributed to manuscript review, editing, and formatting. All authors reviewed and approved the final version of the manuscript. Data Availability The data that support the findings of this study are openly available from public sources. The population mobility data were obtained from Baidu Migration Big Data (https://qianxi.baidu.com/). The socioeconomic data were derived from the Heilongjiang Statistical Yearbook and China Statistical Yearbook, available from the National Bureau of Statistics of China (http://www.stats.gov.cn/). All data used in this study are publicly accessible as described. References Cao Yang. Analysis on Strengthening strategies of Human resource management of rural unemployed [J]. China Market, 2021(5) : 108–109. CAI Lili. Research on the High Quality Development of NEW QUALITY productivity Enabling population [J]. Modern Communication,2025,(02):1–12 + 121. Dale R, O'Rourke T, Humer E, et al. 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Zhu Keli,New Quality productivity and new demographic dividend [J]. Procuratorial Feng Yun,2024,(23):34–35. Zhao Keqin. The Description AND TREATMENT OF UNCERTAINTY BY Set PAIR Analysis [J]. Information and Control, 1995, 24(3): 162–166. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 01 Apr, 2026 Reviews received at journal 24 Mar, 2026 Reviews received at journal 18 Mar, 2026 Reviewers agreed at journal 10 Mar, 2026 Reviewers agreed at journal 10 Mar, 2026 Reviewers invited by journal 23 Feb, 2026 Editor assigned by journal 17 Feb, 2026 Submission checks completed at journal 17 Feb, 2026 First submitted to journal 13 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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distribution\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/4e94c398e24ea24db23008bc.png"},{"id":102853515,"identity":"11c0ebce-afa0-4ee7-a5e1-fee0e42ca71d","added_by":"auto","created_at":"2026-02-17 14:42:16","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":184122,"visible":true,"origin":"","legend":"\u003cp\u003eNetwork Diagram of daily net population migration\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/921be005dffcaa3eb6e5b976.png"},{"id":102853441,"identity":"d07b4bc6-f4f0-4821-a44f-21dfcf60cf8c","added_by":"auto","created_at":"2026-02-17 14:41:49","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":246965,"visible":true,"origin":"","legend":"\u003cp\u003eComparison chart of Gini coefficients in the inflow area and outflow area\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/0ea033517c406d0e40da349e.jpeg"},{"id":102962877,"identity":"fe77444e-00c4-43c7-9c9b-71b1b09528a8","added_by":"auto","created_at":"2026-02-19 04:11:53","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":295851,"visible":true,"origin":"","legend":"\u003cp\u003eTime series comparison of inflow Gini coefficient\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/a4cd9b53d7d941d1c1efd61e.jpeg"},{"id":102853368,"identity":"bf9fb6f2-a377-4073-b0ef-00b34cb3e8b5","added_by":"auto","created_at":"2026-02-17 14:41:38","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":280743,"visible":true,"origin":"","legend":"\u003cp\u003eTime series comparison of outflow Gini coefficient\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/0769e29dc77cd5117f6f6858.jpeg"},{"id":106092896,"identity":"d85b7ea8-f437-4b7e-9013-36bb5ac21ac6","added_by":"auto","created_at":"2026-04-03 11:29:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3513274,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8877013/v1/1333fdb6-f538-4118-97b4-d7a7784a2557.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Integrating set pair analysis and social network analysis to explore the distribution pattern and return flow mechanism of floating population: A case study of Heilongjiang Province, China","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePopulation is the core resource of a city, which can not only promote the development of urban economy, but also promote the prosperity of social culture, which plays a crucial role in the sustainable development of a city. The migration and mobility of population within a certain spatial range can, to some extent, promote the re-aggregation and diffusion of socio-economic elements. From a geographical perspective, the scale of population mobility has become a comprehensive reflection of many economic and social phenomena, such as unbalanced regional economic development and urban-rural dual structure (Pan., 2019). China has a large population that spreads information, capital, and other resources between cities, which not only contributes to the geographical distribution of our population, but also influences our policies, society, and economy. The spatial distribution of population is an important factor to measure the relationship between human development and regional development mode, and the excessive concentration and dispersion of population are the constraints of sustainable urban development (Wang., 2023). Excessive population concentration is accompanied by resource depletion and excess environmental sustainability. Overdispersion of population may lead to unequal regional development along with social resources such as infrastructure, exacerbate the unbalanced development of regions in the process of population mobility, and lead to a cumulative causal cycle of unequal population distribution (Ye., 2020).\u003c/p\u003e \u003cp\u003eIn 2023, General Secretary Xi Jinping first put forward the concept of \"new quality productivity\" during his local inspection.Under the background of the era when new quality productivity has become the core of promoting high-quality development, population, as the most dynamic strategic resource of a city, is deeply integrated with industrial upgrading and scientific and technological innovation, and has become the key factor to promote urban economic and social development. The development of new quality productive forces cannot be separated from the agglomeration and flow of high-quality and highly skilled talents. Talents are not only the main force of technological innovation, but also the promoter of industrial change, which can promote the optimization of urban economic structure and inject strong impetus into urban sustainable development through concept renewal, technology diffusion and knowledge dissemination (Kuang., 2025).\u003c/p\u003e \u003cp\u003eAt present, China is making every effort to promote Chinese-style modernization, and new quality productivity is the core support to achieve this grand goal (Li., 2025). The 20th Report of the Communist Party of China emphasizes the \"modernization with a huge population scale\", which provides a broad human resource base for the development of new quality productive forces. Under the wave of rapid development of new quality productivity, the spatial flow of population in China has accelerated, reshaping the pattern of population distribution. Taking Heilongjiang Province in northeast China as an example, in 2020, the large economic development gap between Heilongjiang Province and other regions accelerated the population outflow. The population of Heilongjiang Province was once in the stage of negative growth. According to the data of the seventh census, the total population of Heilongjiang Province was 31.65\u0026nbsp;million, and compared with the sixth census, the total population of Heilongjiang Province decreased by 6.4\u0026nbsp;million. The average annual growth rate was \u0026minus;\u0026thinsp;1.83 percent, and the rate of negative growth was significantly faster than the national average. Against the background of the gradual decline of the total population, the related problems such as the slowdown of urbanization, the acceleration of population aging and the decline of the birth rate have become increasingly prominent.​ Retain the existing population (Wang., 2021). Therefore, under the dual background of rapid population flow and vigorous development of new qualitative productivity, this paper considers the requirements of Chinese-style modernization development and the strategy of high-quality population development, proposes the set-pair social network analysis method, deeply studies the pattern of national social network, as well as the spatio-temporal characteristics of population flow in Heilongjiang Province, and explores the impact of new qualitative productivity on population flow. To find the population return strategy that meets the development needs of new quality productivity, and provide feasible countermeasures and suggestions for optimizing population structure, cultivating new quality productivity, and realizing the high-quality development of regional economy and society.\u003c/p\u003e"},{"header":"2 Literature review","content":"\u003cp\u003eScholars have carried out systematic research on the spatial distribution of migrant population and formed rich empirical results. Based on the 1982\u0026ndash;1987 census data, Zhang Shan-yu found that China's population migration showed a certain spatial shift, and the migration pattern did not continue the movement from dense areas to sparse areas (Zhang., 1990). Yang Yunyan further revealed that under the effect of the acceleration of urbanization and the difference in regional economic development, the direction of population flow has been fundamentally restructured from the northwest inland to the southeast coast, forming a transformation path from \"extension expansion to connotation agglomeration\" (Yang., 1993). In the era of network analysis, Khanna et al. described the use of complex network analysis methods to study the impact of COVID-19 on India's migrant population (Khanna., 2020), Rajan et al. discussed the vulnerability of COVID-19 to India's migrant population (Rajin., 2020), Dale and others have assessed student mobility during COVID-19 in Austria (Dale., 2021). Zhao Ziyu's team proposed to use the scale of net population flow to explore the characteristics of population mobility during the Spring Festival, and by using the transformation centrality and control measurement model, it was concluded that the population mobility during the Spring Festival travel rush was dominated by inter-provincial migration, and the urban functional status showed hierarchical distribution in the network (Zhao., 2017). In recent years, the research has shown a trend of multi-scale deepening: Liu Xiaoyang's team constructed a spatial-temporal correlation network model of cities around Bohai Sea based on the frequency data of high-speed trains, and found that both regional connection strength and network efficiency had been significantly improved (Liu., 2023). Relying on Tencent migration big data, Zhang Weili's team used complex network analysis to reveal that China's 11 major urban agglomerations show the characteristics of small world inside, and the urban hierarchy shows the evolution characteristics of \"pyramid-shaped\" hierarchical organization structure (Zhang., 2023). Through scale transformation and method innovation, these studies systematically analyzed the evolution mechanism of the spatial distribution of migrant population.\u003c/p\u003e \u003cp\u003eIn terms of the interaction mechanism between the development of new qualitative productivity and population mobility, scholars pointed out that the new qualitative productivity has a significant impact on the decision of population mobility. The development of new quality productivity requires the innovation and optimization of production factors, which promotes the changes of population in entrepreneurial tendency, employment choice, skill upgrading demand and other aspects (Cai., 2025;Zhu., 2024). For example, the emergence of new industries and technologies creates a large number of new jobs and attracts the migrant population with relevant skills, while the traditional mobility model cannot meet the requirements of \"new quality\" of new productivity and promote the optimization and adjustment of labor mobility pattern.\u003c/p\u003e \u003cp\u003eFrom the perspective of regional differences, unbalanced regional development is still a prominent problem restricting China's high-quality development (Peng., 2024). At present, China has the problem of spatial mismatch of urban talents, for example, the \"selection\" effect of big cities leads to insufficient agglomeration of highly skilled talents, and the \"homogeneous\" \"talent war\" leads to insufficient agglomeration of diversified talents, which affects the balanced development of new quality productivity in space.\u003c/p\u003e \u003cp\u003eFor different rural and urban areas, the research also has its own emphasis. In rural areas, the migration of rural population to the cities and the return of some population to the countryside have an impact on the development of rural new quality productivity. In cities, the development of new quality productivity affects the scale, structure and trend of urban population mobility, and cities also need to optimize population structure and enhance urban competitiveness and sustainable development ability by improving new quality productivity.\u003c/p\u003e"},{"header":"3. Data sources, research methods and variable selection","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Data sources\u003c/h2\u003e \u003cp\u003eThe data set of the study comes from an open data source, and the data used is mainly from the big data of migration provided by Baidu, and also refers to the data of China Statistical Yearbook. Migration big data has the characteristics of real-time, objective and comprehensive, and its data accuracy can be traced back to the individual level, so as to compensate for the one-sidedness of the data. This study takes 31 administrative units above the provincial level (referred to as provinces) in China as the research objects, and Taiwan, Hong Kong and Macao Special Administrative Region are not included due to the lack of data availability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Set pair - social network analysis\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Set pair analysis\u003c/h2\u003e \u003cp\u003eSet pair analysis (Zhao., 1995) is a systematic theory and method that uses relation number to deal with uncertainty caused by fuzzy, random, intermediary and incomplete information. It gives objective recognition to all kinds of uncertainty existing objectively, and makes dialectical analysis and mathematical treatment of uncertainty and certainty as a system of identical and different anti-system. It comprehensively describes the relationship between two different things, which is of great significance to the in-depth research and development of system science.\u003c/p\u003e \u003cp\u003eGiven two sets A and B, and suppose that these two sets form the set pair \u003cem\u003eH=(A,B)\u003c/em\u003e, under a specific problem background (let be \u003cem\u003eW\u003c/em\u003e), the characteristics of the set pair \u003cem\u003eH\u003c/em\u003e are analyzed, and \u003cem\u003eN\u003c/em\u003e features are obtained, where: In \u003cem\u003eA\u003c/em\u003e set pair \u003cem\u003eH\u003c/em\u003e, if there are \u003cem\u003eS\u003c/em\u003e features common to sets \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e, sets \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e are opposite on \u003cem\u003eP\u003c/em\u003e features, and on the remaining \u003cem\u003eF\u0026thinsp;=\u0026thinsp;N\u0026thinsp;\u0026minus;\u0026thinsp;S\u0026thinsp;\u0026minus;\u0026thinsp;P\u003c/em\u003e features are neither opposite to each other nor common to both sets, then:\u003c/p\u003e \u003cp\u003e \u003cem\u003ea\u0026thinsp;=\u0026thinsp;S/N\u003c/em\u003e is the same degree of these two sets under the problem \u003cem\u003eW\u003c/em\u003e, referred to as the same degree;\u003c/p\u003e \u003cp\u003e \u003cem\u003eb\u0026thinsp;=\u0026thinsp;F/N\u003c/em\u003e is the dissimilarity degree of these two sets under problem \u003cem\u003eW\u003c/em\u003e, which is called dissimilarity degree.\u003c/p\u003e \u003cp\u003e \u003cem\u003ec\u0026thinsp;=\u0026thinsp;P/N\u003c/em\u003e is the opposite degree of these two sets under problem \u003cem\u003eW\u003c/em\u003e, referred to as opposite degree, then:\u003c/p\u003e \u003cp\u003e \u003cem\u003e\u0026micro;\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;bi+cj\u003c/em\u003e (1)\u003c/p\u003e \u003cp\u003eIt is called the connection degree of two sets \u003cem\u003eA\u003c/em\u003e, \u003cem\u003eB\u003c/em\u003e, and \u003cem\u003ei\u003c/em\u003e, \u003cem\u003ej\u003c/em\u003e is the mark, which is used to distinguish the same degree. Where \u003cem\u003ea\u003c/em\u003e, \u003cem\u003eb\u003c/em\u003e and \u003cem\u003ec\u003c/em\u003e satisfy the normalization condition \u003cem\u003ea\u0026thinsp;+\u0026thinsp;b+c\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eThe three parameters \u003cem\u003ea\u003c/em\u003e,\u003cem\u003eb\u003c/em\u003e and \u003cem\u003ec\u003c/em\u003e in the connection number reflect the same, different and anti-connection degree of the two sets, and the difference of their sizes reflects a certain connection trend of the two sets under the specified problem background, which is defined as the connection potential:\u003c/p\u003e \u003cp\u003eWhen \u003cem\u003ec\u0026thinsp;\u0026ne;\u0026thinsp;0\u003c/em\u003e in connection degree \u003cem\u003e\u0026micro;\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;bi+cj\u003c/em\u003e, the ratio \u003cem\u003ea/c\u003c/em\u003e of the same degree \u003cem\u003ea\u003c/em\u003e and the opposite degree \u003cem\u003ec\u003c/em\u003e is the connection potential of the two sets under the specified problem background, which can be written as follows.\u003c/p\u003e \u003cp\u003e \u003cem\u003eshi (H)\u0026thinsp;=\u0026thinsp;a/c\u003c/em\u003e (2)\u003c/p\u003e \u003cp\u003eWhen \u003cem\u003ec\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e in connection degree \u003cem\u003e\u0026micro;\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;bi+cj\u003c/em\u003e, the ratio of the same degree \u003cem\u003ea\u003c/em\u003e to the difference degree \u003cem\u003eb\u003c/em\u003e is the connection potential of the two sets in the specified problem context, which can be written as follows.\u003c/p\u003e \u003cp\u003e \u003cem\u003eshi (H)\u0026thinsp;=\u0026thinsp;a/b\u003c/em\u003e (3)\u003c/p\u003e \u003cp\u003eThe connection potential energy avoids the imbalance of the same, different and contrary data system caused by different levels and different times. Therefore, this paper uses the connection potential index to describe the intensity of population flow and reflect the spatial relationship of population flow between two provinces. It is used as the initial value of the input matrix of social network analysis, which lays a foundation for the subsequent use of social network analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Social Network Analysis\u003c/h2\u003e \u003cp\u003eSocial network analysis method is a quantitative research tool developed by sociologists based on mathematical methods and graph theory. This method systematically analyzes the structural characteristics and interaction rules of the relationship network between social entities by constructing a node and connection model. In this paper, the method of social network analysis will be used to construct the spatial relationship model of population flow with cities as nodes and inter-city population flow as links, to deeply explore the structural characteristics and hierarchical relationship of population flow network between different regions in the development process of new qualitative productivity, and to reveal the internal relationship between population flow and the development of new qualitative productivity. Commonly used network analysis metrics include:\u003c/p\u003e \u003cp\u003e(1) degrees\u003c/p\u003e \u003cp\u003eDegree can describe the state of interconnection between nodes, thus reflecting the evolution characteristics of the network (Neal., 2011). In the directed network, it is divided into two concepts: in-degree and out-degree. In this paper, only in-degree is considered in the study of backflow population. There are different in-degrees in the mobility network of urban nodes, which represent the attractiveness and radiation force of the city under a certain measurement standard. The calculation formula is as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\text{W}}_{\\text{m}\\text{i}}\\text{=}\\sum\\:_{\\text{k}\\text{=1}}^{\\text{n}}{\\text{R}}_{\\text{mk}\\text{j}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{W}}_{\\text{m}\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e represents the total indegree value of city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in the study period, and \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emkj\u003c/em\u003e\u003c/sub\u003e represents the value of the path that generates inflow relationship between other cities and city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in day \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{j}\\)\u003c/span\u003e\u003c/span\u003e.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\text{W}}_{\\text{mo}}\\text{=}\\sum\\:_{\\text{k}\\text{=1}}^{\\text{n}}{\\text{R}}_{\\text{mkj}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{W}}_{\\text{mo}}\\)\u003c/span\u003e\u003c/span\u003e represents the total outdegree value of city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in the study period, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{R}}_{\\text{mkj}}\\)\u003c/span\u003e\u003c/span\u003erepresents the value of the path that city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e generates outflow relationships with other cities in day \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{j}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e(2) Betweenness centrality\u003c/p\u003e \u003cp\u003eBetweenness centrality reflects the influence and control of a city when it interacts with other cities in the population flow network. Nodes with higher betweenness centrality are more important in the network and have stronger control ability over other nodes, which can be calculated as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{e}}_{\\text{m}}\\text{=}\\sum\\:_{\\text{\u0026nu;}\\text{\u0026ne;}\\text{m}}\\frac{\\text{n}\\text{(}\\text{u}\\text{,}\\text{v}\\text{|}\\text{m}\\text{)}}{\\text{n}\\text{(}\\text{u}\\text{,}\\text{v}\\text{)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{n}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e(\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{u}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{v}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e is the number of shortest paths between node \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cem\u003ev\u003c/em\u003e, and \u003cem\u003en(\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{u}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{v}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e|\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e is the number of shortest paths between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{v}\\)\u003c/span\u003e\u003c/span\u003e connected by node \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{m}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e(3) The clustering coefficient\u003c/p\u003e \u003cp\u003eClustering coefficient reflects the degree of interconnection between nodes (WEI., 2016). When some nodes are particularly closely linked together, a network community can be formed.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\text{C}}_{\\text{i}}\\text{=}\\frac{\\text{2}{\\text{B}}_{\\text{i}}}{{\\text{m}}_{\\text{i}}\\text{(}{\\text{m}}_{\\text{i}}\\text{\u0026minus;1)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the clustering coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the number of edges that actually exist between the neighbor nodes of node \u003cem\u003ei\u003c/em\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the number of paths between node \u003cem\u003ei\u003c/em\u003e and its neighbors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3 Set Pair Social Network Analysis and its process\u003c/h2\u003e \u003cp\u003eSet pair social network analysis combines set pair analysis with social network analysis. It uses set pair analysis to calculate the connection degree between data, so as to obtain the connection potential between data, which is used as the relationship structure value in social networks to calculate network analysis indicators and study network relationships. The set pair analysis method is used to improve the social network analysis, and the network characteristics are enhanced by optimizing the social network data, so as to construct the population mobility network analysis model. In terms of specific measurement, this paper regards the directional characteristics in the data as the uncertain characteristics of the identical, different and contrary relationship in the set pair, and regards the directional uncertainty relationship and the numerical certainty relationship in the population flow data as a system. It studies the value law of the directional characteristics under specific conditions, and quantifies them into the population flow data to comprehensively describe the population flow relationship between two provinces.\u003c/p\u003e \u003cp\u003eTraditional social network analysis usually simplifies the relationship between nodes to deterministic directed or weighted connections when dealing with the problem of population flow, and its essential assumption is that the strength and direction of the flow relationship are statistically stable and fully observable. However, in the study of population mobility based on migration big data, the relationship between nodes often has the characteristics of directional asymmetry, intensity fluctuation and statistical incompleteness at the same time. It is easy to ignore the implied intermediary states and fuzzy relationships in the process of population mobility simply by describing the flow scale or weighting matrix, which weakens the expression ability of network structure features.\u003c/p\u003e \u003cp\u003eThe specific process is as follows:\u003c/p\u003e \u003cp\u003e(1) Determine the set pair according to the research content, and select the characteristics of the set pair data. The research content of this paper is the population flow between provinces, so the two provinces are combined into a set pair, and the direction characteristics of the population flow data between provinces are selected.\u003c/p\u003e \u003cp\u003e(2) The characteristics of the data are summarized and the attributes are divided. In this study, the directional characteristics of four population flow data for each province are summarized as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below, and the attributes are divided and defined as the same degree a and the difference degree b.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(3) According to the characteristics of same degree and difference degree determined above, calculate the connection degree according to Formula (1). In this study, each province is defined as a set, and any two provinces form a set pair \u003cem\u003eH\u003c/em\u003e. Considering the directional characteristics of population flow data, the characteristics are summarized and divided into attributes. The \u003cem\u003ea\u003c/em\u003e is the same characteristics shared by the two provinces, \u003cem\u003eb\u003c/em\u003e is the characteristics that are neither the same nor different between the two provinces, and \u003cem\u003ec\u003c/em\u003e is 0 because there are no different characteristics. It is combined into the same, different and contrary system to calculate the connection number \u003cem\u003e\u0026micro;\u003c/em\u003e, quantify the data characteristics, and comprehensively describe the connection between two provinces.\u003c/p\u003e \u003cp\u003e(4) Calculate the contact potential according to Eq.\u0026nbsp;(3), and use the contact potential as social network data to construct the correlation matrix of population mobility. The connection potential can avoid the characteristics of data imbalance caused by different levels and different times. Therefore, this paper uses the connection potential index to describe the intensity of population flow and reflect the spatial relationship of population flow between two provinces.\u003c/p\u003e \u003cp\u003e(5) The calculated contact potentials are used as social network data, and the spatial relationship matrix represents the flow characteristics of the population in a day.\u003c/p\u003e \u003cp\u003e(6) The calculated initial matrix of spatial relationship is binarized and used as the input matrix of social network analysis, and the clustering coefficient and network centrality parameters of population flow between provinces are obtained through UCINET. At the same time, the UCINET input matrix is imported into the visualization tool ArcGIS. A specific graphical representation of the results of the population mobility network can be directly observed.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Measurement of hierarchical characteristics of population mobility network\u003c/h2\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Population offset growth\u003c/h2\u003e \u003cp\u003eThe shift-share method was proposed by Creamerl earlier and has been widely used in the study of regional economic growth and population pattern evolution. Among them, \"sharing\" refers to the amount of growth obtained according to the regional growth rate, and \"offset\" refers to the difference between absolute growth and shared growth. The formula is as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{s}\\text{h}\\text{if}{\\text{t}}_{\\text{i}}\\text{=}\\text{absg}{\\text{r}}_{\\text{i}}\\text{\u0026minus;}\\text{s}\\text{h}\\text{ar}{\\text{e}}_{\\text{i}}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\text{=}\\text{po}{\\text{p}}_{\\text{i}}\\text{(}{\\text{t}}_{\\text{1}}\\text{)\u0026minus;}\\frac{\\sum\\:_{\\text{i}\\text{=1}}^{\\text{n}}\\text{p}\\text{o}{\\text{p}}_{\\text{i}}\\text{(}{\\text{t}}_{\\text{i}}\\text{)}}{\\sum\\:_{\\text{i}\\text{=1}}^{\\text{n}}\\text{pop}\\text{(}{\\text{t}}_{\\text{0}}\\text{)}}\\text{\u0026times;}\\text{po}{\\text{p}}_{\\text{i}}\\text{(}{\\text{t}}_{\\text{0}}\\text{)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:shif{t}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:absg{r}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:shar{e}_{i}\\)\u003c/span\u003e\u003c/span\u003e respectively represent the offset growth, absolute growth and shared growth of population of city \u003cem\u003ei\u003c/em\u003e in the time period of (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{0}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{1}\\)\u003c/span\u003e\u003c/span\u003e),\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:po{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the total population of the city,\u003cem\u003en\u003c/em\u003e denotes the number of cities. Positive offset growth indicates a strong population agglomeration ability, and vice versa a weak population agglomeration ability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Gini coefficient\u003c/h2\u003e \u003cp\u003eGini coefficient(Liu., 2016) first appeared in the field of income distribution difference research, and subsequent studies have extended it to quantitative analysis of the characteristics of unbalanced spatial distribution of population. In this study, the method is introduced into the evaluation of the equilibrium of the spatial distribution of the outflow population. By calculating the distribution difference of the outflow scale between different regions, the spatial agglomeration degree and dynamic change characteristics of the population flow are objectively measured. The calculation formula is as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\text{G}\\text{=1\u0026minus;}\\frac{\\text{1}}{\\text{n}}\\text{(2}\\sum\\:_{\\text{i}\\text{=1}}^{\\text{n}\\text{\u0026minus;1}}{\\text{w}}_{\\text{i}}\\text{+1}\\text{)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{G}\\)\u003c/span\u003e\u003c/span\u003e is Gini coefficient, and the value is between 0 and 1. The larger the value is, the more concentrated the spatial distribution of the outflow population is.On the contrary, the more dispersed it is.;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{w}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e represents the proportion of the population flowing into region \u003cem\u003ei\u003c/em\u003e to the total outflow, and \u003cem\u003en\u003c/em\u003e represents the number of regions.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 New mass gravity-population mobility response model\u003c/h2\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.4.1 Baseline regression models\u003c/h2\u003e \u003cp\u003eOn the basis of controlling regional heterogeneity and time effect, this paper accurately identifies the influence of new quality productivity on population mobility. Based on the data of population mobility and new quality productivity development in Heilongjiang Province, this paper establishes a bilateral fixed effect regression model to systematically test the driving effect of the two from the measurement level, so as to realize the mechanism expansion and deepening of the above spatial pattern analysis results. The reflow strategy is put forward.\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{\\text{NPI}}_{\\text{it}}\\text{=}{\\text{a}}_{\\text{0}}\\text{+}{\\text{a}}_{\\text{1}}{\\text{NQP}}_{\\text{it}}\\text{+}{\\text{a}}_{\\text{2}}\\text{ln}{\\text{C}\\text{ontrol}}_{\\text{it}}\\text{+}{\\text{\u0026mu;}}_{\\text{t}}\\text{+}{\\text{v}}_{\\text{i}}\\text{+}{\\text{\u0026epsilon;}}_{\\text{it}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{NPI}\\)\u003c/span\u003e\u003c/span\u003e is the net population flow, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{NQP}\\)\u003c/span\u003e\u003c/span\u003e is the level of new quality productivity,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{C}\\text{ontrol}\\)\u003c/span\u003e\u003c/span\u003e is the set of control variables,\u003cem\u003ei\u003c/em\u003e is the city,\u003cem\u003et\u003c/em\u003e is the year,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{\u0026mu;}}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e is the individual fixed effect,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{v}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the time fixed effect, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{\u0026epsilon;}}_{\\text{it}}\\)\u003c/span\u003e\u003c/span\u003e is a random term.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.4.2.Variable selection\u003c/h2\u003e \u003c/div\u003e \u003c/div\u003e\n\u003ch3\u003e1. Explained variables\u003c/h3\u003e\n\u003cp\u003eIn this paper, the net population flow(NPI) is used as the explained variable, which is obtained by using the permanent population-registered population between regions. It can intuitively reflect the population attraction and flow direction of a single city, facilitate the comparison of the change trend of floating population between different cities, and can more accurately reflect the impact of the level of new quality productivity on population flow, and reflect its comprehensive impact on labor inflow and regional development.\u003c/p\u003e\n\u003ch3\u003e2. Core explanatory variables\u003c/h3\u003e\n\u003cp\u003eThe core explanatory variable of this paper is the development level of new quality productivity(NQP). The new quality productivity evaluation index system is constructed from the three aspects of workers, labor objects and labor materials, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The entropy method is used to synthesize the measures.\u003c/p\u003e \u003cp\u003eTo understand the level of new quality productivity, we should mainly explore from three aspects: workers, labor objects and labor materials. As the core driving force, workers are high-quality talents with advanced technology and innovation ability. Through research and development, knowledge application and model innovation, they can promote the high-quality development of new productive forces. The labor object is the material foundation, the new labor object expands the production boundary, the high quality labor object can improve the product quality, and promote the development of green industry. Labor materials are technical support, and advanced production tools and equipment support technological innovation, reduce costs, optimize production processes, promote industrial integration, and give birth to new forms of business. The three are interconnected and synergistic, promoting productivity to break through the traditional development path, and building a new quality productivity system with innovation as the core, high-tech and high-quality characteristics.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMeasurement Index System of New Productive Forces\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFirst level indicator\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003esecond-level indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIndicator Meaning\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eLaborer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSupply and quality of human capital\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of regular institutions of higher learning\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of employees in strategic emerging industries\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAverage wage of employees on the job\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eMain output of innovation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of inventions filed in the current year\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of utility models applied in the current year\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of green inventions filed that year\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of green utility models applied in that year\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003elabor object\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eData element resources\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLevel of utilization of data elements\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWhether there is a data trading platform\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCarbon trading/energy trading volume\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEcological environment resources\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHarmless disposal rate of household garbage\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInvestment in environmental pollution control\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003elabor material\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDigital infrastructure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of Internet broadband access users\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal amount of telecommunications services\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIntelligent technical equipment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRobot mounting density\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of AI enterprises\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInnovation input guarantee\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe proportion of science expenditure in local fiscal expenditure\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003e3. Control variables\u003c/h3\u003e\n\u003cp\u003eThe control variables and measurement methods of this paper are as follows: (1) Economic development level (EDL), represented by per capita regional product; (2) Financial development level (FDL), the balance of deposits and loans of financial institutions at the end of the year/regional GDP; (3) The level of opening to the outside world (OPEN), which is obtained by the amount of foreign capital actually utilized/GDP of the region; (4) The degree of government intervention (GOV), the expenditure in the general budget of local finance/regional GDP; (5) Industrial structure (IND), the value added of the tertiary industry/GDP. In this paper, the log form of continuous control variables is taken to reduce skewness and mitigate the impact of extreme values.\u003c/p\u003e\n\u003ch3\u003e4. Descriptive statistics of data\u003c/h3\u003e\n\u003cp\u003eIn order to eliminate the dimensional differences, the explained variables are standardized by range, and the descriptive statistics are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e below:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive Statistics of Variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMtandard deviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNPI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNQP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.239\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10.429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.478\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.434\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.905\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.678\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.588\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.586\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOPEN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGOV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.675\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIND\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.677\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4 Empirical analysis","content":"\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Analysis of spatio-temporal evolution of provincial population mobility based on set pair association network\u003c/h2\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e4.1.1 Degree value analysis\u003c/h2\u003e \u003cp\u003eBased on the degree value analysis of the spatial correlation network structure of China's inter-provincial population mobility, the network structure is stable and the index fluctuation is small during the study period, so only the data in 2023 are selected for analysis. Ucinet software is used to calculate the degree value of population mobility network in 31 provincial-level administrative regions, and it is found that the degree centrality is within the interval [0,15], and the differences in spatial connections between provinces lead to unbalanced population mobility, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eGuangdong province, Jiangsu Province and other top ten provinces in terms of point access degree, whose degree values are higher than the national average, play a key role in the population mobility network and become the core of network cohesion and integration. Relying on the advantages of economy, geography, resources and transportation, these provinces show significant siphon effect, which not only has a strong attraction, but also forms an aggregation effect.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCharacteristics of Entry and Exit\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProvinces\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePoint out degree\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoint in degree\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGuangdong Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJiangsu Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCity of Tianjin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHubei Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZhejiang Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShanghai City\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSichuan Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHunan Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBeijing City\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShandong Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section3\"\u003e \u003ch2\u003e4.1.2 Betweenness centrality analysis\u003c/h2\u003e \u003cp\u003eThe betweinness centrality reflects the transportation capacity and aggregation capacity of each province in the population mobility network. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e that the nodes with high centrality in the middle of population mobility are mainly located in the eastern region, with them as the center and scattered around, showing a core-periphery structure, and the centrality and total degree of provincial administrative regions are positively correlated. The greater the intermediate centrality is, the more the province is in the core position, and it has the control advantage to control the communication of all other points, which can play the role of a bridge connecting all provinces. It can be seen from the figure that the intermediate centrality of Beijing, Tianjin and Shanghai is relatively large, and the centrality of Shanghai is the first in the three periods. It can be seen that regions with slow development of new quality productivity, such as Heilongjiang Province, are at the edge of the network, with little connection effect and unable to control the interaction of other points.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003e4.1.3 Cluster coefficient analysis\u003c/h2\u003e \u003cp\u003eAs a key indicator to measure the clustering characteristics of network nodes, the clustering coefficient reflects the local density of connections between nodes. The research shows that the average clustering coefficient of population mobility network in provincial administrative areas in China in 2019, 2021 and 2023 is over 0.5, higher than that of random network, and the network path length is stable at about 2.0, showing the typical characteristics of small world network. This feature of \"high cluster-short path\" not only means that the population mobility network has efficient information transmission efficiency, but also provides a structural basis for the cross-regional mobility and collaborative innovation of new quality productivity factors. The short path feature promotes the rapid diffusion of innovation elements and the balanced development of new quality productivity among regions.\u003c/p\u003e \u003cp\u003eCommunity structure theory, which emphasizes the stable association and dynamic evolution of elements within a system, has been widely used in the study of complex networks in recent years. Through the modular cluster analysis of the inter-provincial population mobility network by Gephi software, it is found that the country can be divided into four communities: northeast - North China, Northwest China, East - South China, and southwest - South China, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Provinces within the same community are closely connected in space, which reflects the restriction of geospatial effect on population mobility. From the perspective of new quality productivity, this community structure provides opportunities for regional coordinated development. For example, the northeast and North China communities where the three northeastern provinces are located are spatially adjacent to each other, which is conducive to the construction of a collaborative development circle of new quality productivity and the acceleration of technological innovation and achievement transformation through industrial complementarity and resource sharing. The strengthening of the trend of population mobility across large-scale geographical space will further promote the optimal allocation of new qualitative productivity factors, promote Heilongjiang and other old industrial bases to use external innovation resources, accelerate the transformation and upgrading of traditional industries, improve the allocation of social resources, and inject new momentum into the cultivation and development of new qualitative productivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Calculation of hierarchical characteristics of population mobility network in Heilongjiang Province\u003c/h2\u003e \u003cdiv id=\"Sec25\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1 Situation and stage characteristics of population mobility\u003c/h2\u003e \u003cp\u003eThe dynamic evolution of the spatial pattern of migrant population is essentially the mapping result of the heterogeneity of regional growth at different administrative levels in the spatial dimension. Therefore, in order to deeply analyze the dynamic evolution mechanism of the spatial distribution of migrant population, it is necessary to start from the spatial expression of the growth difference of multi-scale regional migrant population, quantitatively analyze the spatial differentiation characteristics of the growth intensity among regions, and reveal the internal driving factors of the spatial pattern of population migration. The dynamic evolution of the spatial distribution pattern of regional floating population is caused by the offset growth of each region and its subordinate provinces. Based on this, to explore the evolution trajectory of the spatial pattern of migrant population, it is necessary to start from the migration growth characteristics of the migrant population in each region and its subordinate provinces. And the specific performance of the growth rate. The spatial distribution of the migration growth of China's migrant population from 2013 to 2022 is obtained through calculation, and the specific data are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Based on these data, this paper sorts out the main clues of the evolution of the spatial pattern of China's floating population, explores the relationship between the migration growth rate of Heilongjiang Province and other provinces, and reveals its internal rules and characteristics.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1 Migration and Growth of Floating Population in Various Regions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eEastern region\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eCentral region\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eWestern region\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eNortheast region\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBeijing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e266.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHenan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e98.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eInner Mongolia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e55.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eLiaoning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e90.59\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTianjin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHubei\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-64.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYunnan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-7.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eJi Lin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-123.96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHebei\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-15.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHunan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-29.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSichuan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-89.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHeilongjiang\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-26.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShandong\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35.026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eJiangxi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-74.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGuizhou\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-182.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShanghai\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e112.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnhui\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e198.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eChongqing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJiangsu\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e37.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShanxi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e126.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eShaanxi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-167.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZhejiang\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e244.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGansu\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-98.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFujian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-26.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eQinghai\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-10.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGuangdong\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-140.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNingxia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-9.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHainan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-57.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXinjiang\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-5.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGuangxi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-119.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXizang\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-6.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal amount\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e462.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal amount\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e254.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTotal amount\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-636.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTotal amount\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-59.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSince 2013, the migration growth of migrant population in all provinces in China has maintained a stable situation in terms of overall scale and growth intensity. The data show that the total number of migrant population in China increased by 92,472,200 during this period, indicating that the growth of migrant population during this period showed a significant expansion trend due to the factor mobility vitality brought by the development of new quality productivity. From the regional dimension, although the overall evolution trend of the migration growth of migrant population in the four regions has a certain synchronicity, there are obvious spatial differences in the growth intensity under the influence of the spatial heterogeneity of the development level of the new quality productivity, which reflects the regional differentiation of the traction and remodeling effect of the new quality productivity on population migration.\u003c/p\u003e \u003cp\u003eThe migration growth of floating population in Heilongjiang is \u0026minus;\u0026thinsp;26.10, showing a trend of population outflow. From the perspective of new quality productivity, this is related to the development level of regional new quality productivity. If the cultivation of emerging industries and the agglomeration of innovation factors are insufficient, the upgrading of traditional industries will be slow, and the attraction of employment and development space to the population will weaken. At the same time, it is also necessary to pay attention to its distribution potential in the fields of new quality productivity such as digitalization of ice and snow economy and intelligence of energy industry. If high-quality employment and development opportunities can be created by developing new industries such as smart agriculture and green energy, it is expected to optimize the pattern of population mobility and realize the two-way empowerment of population and new quality productivity development.\u003c/p\u003e \u003cp\u003eThe spatial network diagram drawn by ArcGIS shows that in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the population flow in Heilongjiang Province in 2019, 2021 and 2023 shows a pattern of \"dense in the east and sparse in the west,\" which has both the characteristics of proximity and jump, and is closely related to the development of new quality productivity. As a core factor, population's mobility pattern affects innovation, factor allocation and industrial upgrading, and accelerates the spread of knowledge and technology. The population flow between Heilongjiang and Liaoning, Beijing, Jilin and other neighboring regions promotes the sharing of innovative resources and the absorption of technological ideas, and provides energy for industrial innovation. Due to the close space and complementary industries among neighboring provinces, the synergy between labor and technology can be realized to promote industrial upgrading. Although there is a short-term brain drain in the population flow between Heilongjiang and the eastern provinces, it is conducive to the introduction of experience, technology and capital, the transformation of traditional industries, and at the same time, it gives full play to its own resource advantages to attract innovative factors and promote regional coordinated development. By guiding the reasonable flow of population, optimizing the allocation of resources and deepening regional cooperation, we can fully release its role in promoting the new quality productivity and help Heilongjiang's high-quality economic development.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2 Gini coefficient measurement of spatial agglomeration characteristics of population out-migration in Heilongjiang Province\u003c/h2\u003e \u003cp\u003eAs the core index to measure the spatial agglomeration effect of industry, the theoretical origin of spatial Gini coefficient can be traced back to the pioneering research of Plane et al in the 1990s. This study introduces the Gini coefficient method into the analysis of the spatial pattern of population mobility, and provides a new idea for analyzing the spatial heterogeneity of population mobility by quantifying the concentration degree of population inflow and outflow between regions. The coefficient ranges from 0 to 1, and the larger the value is, the more significant the regional difference is, the higher the regional concentration of migrant population is, and the more prominent the non-equilibrium characteristics of population distribution are. This index can effectively describe the agglomeration characteristics of the spatial distribution of population.Therefore, this paper uses the Gini coefficient to analyze the regional characteristics of the inter-provincial out-migration of Heilongjiang's population, as shown in Table\u0026nbsp;5.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGini Coefficient\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRegion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2023\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eFlows into Heilongjiang Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEastern region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7504\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7517\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.7540\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCentral Region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5471\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWestern region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.6215\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOutflow from Heilongjiang Province\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEastern region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.7512\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCentral Region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5927\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5976\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWestern region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6426\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.6867\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eNumerically, relying on the agglomeration of new quality productivity in the Pearl River Delta, Yangtze River Delta and Beijing-Tianjin-Hebei urban agglomerations in the eastern region in 2019, the population inflow and outflow in Heilongjiang Province show the characteristics of high spatial agglomeration, and the Gini coefficients are 0.7504 and 0.7296 respectively. Affected by the regional differences of new quality productivity, the distribution of population mobility in the western region is relatively uneven. The development of new quality productivity in the central region is relatively balanced, and the difference in population mobility is small.In 2022,the coordinated and balanced development of new quality productivity in the central and western regions will promote the distribution of population mobility to become more uniform, and the relevant Gini coefficient will decrease significantly, while the agglomeration effect in the eastern region will be further strengthened.In 2023, with the strengthening of regional differentiation and agglomeration effect of the new qualitative productivity, the Gini coefficient of population inflow and outflow in the eastern, central and western regions of Heilongjiang Province shows an upward trend, indicating that the regional heterogeneity of the new qualitative productivity continues to deepen the spatial agglomeration pattern of population flow. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e intuitively shows the agglomeration differences between the population inflow and outflow regions in 2023.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig.\u0026nbsp;7 respectively show the time series distribution characteristics of population inflow and population outflow, in which the color depth of the color block is positively correlated with the value size. The longitudinal analysis based on the time dimension shows that at the eastern regional level, no matter Heilongjiang province is the place of population inflow or outflow, its Gini coefficient shows an upward trend, indicating that the equilibrium of population distribution in this region has been improved. Specifically, due to the migration of population from a large number of regional provinces to Heilongjiang Province in the eastern region, the spatial distribution balance of the outflow population is significantly enhanced. At the central region level, the Gini coefficient of the population migration from provinces to Heilongjiang Province shows the fluctuation characteristics of falling first and then rising, while the Gini coefficient of the population inflow continues to rise. This change shows that the migration activities of the central provinces lead to the simultaneous increase of the imbalance in the distribution of the outflow and inflow of the population. In the western region, the Gini coefficients of population inflow and outflow show a U-shaped curve characteristic of first decreasing and then increasing, which reflects that the distribution imbalance of urban population migration in this region has experienced a dynamic process of \"aggravation-relief-aggravation\", and finally shows an overall upward trend.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5. Test and strategy derivation of reflow mechanism driven by new quality productivity","content":"\u003cp\u003eIn the context of new quality productivity, population return is not a short-term random behavior, but the result of the combined effect of long-term institutional environment, public services and regional development differences.Different regions have significant differences in resource endowment, historical development path and institutional environment,and these unobservable but relatively stable individual characteristics, as well as macroeconomic fluctuations, policy adjustments and other factors,will affect population mobility.\u003c/p\u003e \u003cp\u003eTherefore, on the basis of controlling regional heterogeneity and time effect, this paper accurately identifies the net effect of the new quality productivity on population mobility. In this way, the mechanism of the above analysis results of the spatial pattern of migrant population can be expanded and deepened. This model provides a reliable empirical basis for the formulation of subsequent population return policy.\u003c/p\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Benchmark regression results\u003c/h2\u003e \u003cp\u003eAs can be seen from the benchmark regression results, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, the new quality productivity has a significantly negative impact on the net population flow of Heilongjiang Province. This result itself has a strong \"counterintuitive\" feature: referring to the mainstream development economics and population mobility theory, the improvement of productivity usually means the improvement of employment opportunities and the increase of income expectations, thus attracting the population. Considering the realistic background from 2012 to 2022, the improvement of new quality productivity in Heilongjiang Province does not rely on the expansion of population intensive industries, but is more reflected in digitalization, automation, capital deepening and the agglomeration of a few high-end technology sectors. This kind of new-quality productivity has the characteristics of \"low employment elasticity\" : on the one hand, it compresses the employment space of traditional manufacturing and resource-based industries through technological substitution; On the other hand, highly skilled labor continues to flow efficiently to the well-developed eastern coastal areas, but the new jobs have high requirements on human capital, and the mismatch with the local labor structure is obvious, which ultimately leads to the phenomenon of continuous population outflow despite the good development of productivity.\u003c/p\u003e \u003cp\u003eFrom Model (2), after the control variables are added, the absolute value of NQP coefficient converges but is still significantly negative, indicating that the above mechanism is not explained by other macro factors, but the endogenous result of the new quality productivity itself in the development stage of Heilongjiang Province. It is particularly noteworthy that the industrial structure variable (IND) is also significantly negative, indicating that industrial transformation and upgrading does not form a positive pull on the population in the short term. Furthermore, the variables of education level and financial development do not show a significant impact, which to a certain extent reflects the problem of human capital spillover rather than agglomeration in Heilongjiang Province. At the same time, the insignificant degree of opening up and government intervention also implies that the marginal effect of traditional policy tools in dealing with the impact of new-quality productivity on population mobility is limited.\u003c/p\u003e \u003cp\u003eBased on the experience of Heilongjiang Province, the new quality productivity does not naturally have the effect of population attraction, and its impact on population mobility is highly dependent on the matching degree of regional industrial carrying capacity and labor force structure. The result revealed by the benchmark regression is not a simple conclusion that the new quality productivity inhibits the population inflow, but a deeper structural fact. This finding not only provides a new explanatory framework for understanding the population mobility in Heilongjiang Province, but also puts forward an important reflection on the current regional development policy focusing on the new quality productivity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBenchmark Regression Results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel (1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModel (2)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNQP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-4.041\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-3.490)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.037\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.350)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.031\u003c/p\u003e \u003cp\u003e(-0.920)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.038\u003c/p\u003e \u003cp\u003e(-1.600)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOPEN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-7.836\u003c/p\u003e \u003cp\u003e(-1.360)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGOV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.076\u003c/p\u003e \u003cp\u003e(0.930)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIND\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.263\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.980)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant term\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.596\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(16.76)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.054\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(2.680)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.397\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Robustness test\u003c/h2\u003e \u003cdiv id=\"Sec30\" class=\"Section3\"\u003e \u003ch2\u003e5.2.1 Add lagged term of explained variable\u003c/h2\u003e \u003cp\u003eConsidering the possible inertial characteristics of population flow, this paper introduces the one-period lagged term of net population flow into the benchmark model for robustness test. As shown in Model (1) and Model (2) in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the regression coefficients of new quality productivity are significantly negative regardless of whether control variables are added, and the significance level is consistent with the benchmark regression, indicating that the above conclusions are not caused by short-term fluctuations or endogeneity problems. It can be seen that the inhibitory effect of the new quality productivity on the net population flow in Heilongjiang Province has certain continuity and stability, and the population outflow will not be automatically weakened with the passing of time.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section3\"\u003e \u003ch2\u003e5.2.2 Adding control variables\u003c/h2\u003e \u003cp\u003eAfter the control variables of economic density(ED) and medical and health care level(MHL) are further introduced on the basis of the benchmark model, although the estimated coefficient of the new quality productivity has changed, the sign and significance have not changed fundamentally. At the same time, the newly added control variables fail to significantly change the direction of population flow, indicating that the continuous outflow of population in Heilongjiang Province is not solely restricted by public services or spatial conditions, but is closely related to the structural development model led by the new quality productivity. In general, the robustness test results are consistent with the previous analysis.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of Robustness tests\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel (1), the explained variable is lagged by one period\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModel (2), the explained variable is lagged by one period\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModel (3) adds control variables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModel (4) adds control variables\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNQP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-5.290\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-3.810)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.809\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.940)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.041\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-3.490)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.822\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.190)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.045\u003c/p\u003e \u003cp\u003e(-1.140)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.142\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(2.100)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.048\u003c/p\u003e \u003cp\u003e(-1.710)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.044\u003c/p\u003e \u003cp\u003e(-1.580)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOPEN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-9.136\u003c/p\u003e \u003cp\u003e(-1.340)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-6.853\u003c/p\u003e \u003cp\u003e(-1.210)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGOV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.133\u003c/p\u003e \u003cp\u003e(1.400)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003cp\u003e(0.320)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIND\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.290\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.290)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.345\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-3.370)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eED\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.204\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-2.430)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMHL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.035\u003c/p\u003e \u003cp\u003e(-0.380)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant term\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.630\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(14.75)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.247\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(2.550)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.596\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(16.76)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003cp\u003e(1.240)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e156\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.526\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.434\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Heterogeneity analysis\u003c/h2\u003e \u003cp\u003ePopulation density, as an important indicator to measure the level of urban population agglomeration, reflects the intensity of urban economic activities, the improvement of infrastructure and the supply capacity of public services to a certain extent. Areas with high population density usually have stronger factor agglomeration capacity and more perfect supporting conditions for employment and living, while areas with low population density have constraints such as insufficient attraction to factors. Based on this, this paper groups the samples according to the population density level of cities, and divides the top six cities in population density into the high population density group, and the remaining cities into the low population density group, so as to examine the difference in the effects of the two under different population agglomeration levels, so as to reveal the heterogeneity characteristics behind the average effect.The heterogeneity results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe regression results show that the impact of new quality productivity on net population flow is significantly different in cities with different population density. In cities with high population density, the regression coefficient of the new quality productivity variable is still negative and significant at the 1% significance level, which is consistent with the results of the whole region. In contrast, in cities with low population density, the impact of new quality productivity on net population flow is significantly positive, that is, the development of new quality productivity significantly promotes population return and net population inflow.\u003c/p\u003e \u003cp\u003eThis result shows that the new quality productivity does not produce a consistent population effect among different cities, and its direction and intensity of influence obviously depend on the population agglomeration level of the city. For cities with high population density, their original population carrying capacity and factor agglomeration level are already at a high state, and the development of new quality productivity is more reflected in technological upgrading and industrial efficiency improvement, with limited marginal absorption capacity for new population, and may even strengthen population outflow by increasing living costs and competitive pressure. For cities with low population density, the development of new quality productivity significantly enhances the ability to attract population by cultivating emerging industries, expanding employment space and improving development expectations, thus effectively promoting population return. Combined with the benchmark regression results, it can be found that the average effect of the new quality productivity on the net population flow in the overall sample is essentially the accumulation of the opposite effects in the above two types of cities.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of Heterogeneity Analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel (1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModel (2)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNQP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-5.646\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(-7.090)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.939\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(2.790)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant term\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.742\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(18.46)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.466\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(61.460)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.175\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6 Conclusion: New quality productivity-oriented population return strategy","content":"\u003cp\u003eFrom the perspective of new quality productivity, this paper systematically reveals the network pattern and regional differences of population migration in China, and takes Heilongjiang Province as an example to empirically analyze the action mechanism of new quality productivity on population backflow. The results show that the national population mobility network presents a stable small-world structure and significant core-periphery differentiation characteristics, and the regions with higher new quality productivity have stronger ability to attract and control population in the network.\u003c/p\u003e \u003cp\u003eIn addition, Heilongjiang Province has been at the edge of the population mobility network for a long time, and the characteristics of population outflow are obvious. The measurement results show that the new quality productivity has a negative impact on the overall net population flow in Heilongjiang Province, which is rooted in the mismatch between the development stage of the new quality productivity and the local labor structure. It can be seen that the impact of the new quality productivity on population mobility is obviously situational dependent, and it is necessary to promote the co-evolution of the new quality productivity and high-quality population development by optimizing the industrial carrying capacity, reducing the living cost and improving public services. Based on the above research conclusions, policy recommendations are put forward:\u003c/p\u003e\n\u003ch3\u003e1. Accelerate the development and improvement of the technology market and reduce the risk gap.\u003c/h3\u003e\n\u003cp\u003eThe large-scale outflow of population in Heilongjiang Province will inevitably lead to the loss of human resources, which directly leads to the lack of technical talent reserves in various industries in the province. The lagging technological competitiveness further weakens the attractiveness of technical talents in Heilongjiang Province, thus forming a vicious circle, which not only seriously restricts the economic development vitality of Heilongjiang Province, but also aggravates the unemployment risk and health risk faced by the returning population. In order to prevent and control health risks, it is necessary to build a more sound social security network system and strengthen the supply of public health services. In terms of unemployment risk, returnees may encounter problems such as poor connection of human resources, insufficient support for entrepreneurship and employment, and disconnection between personal skills and market demand (Cao., 2021).\u003c/p\u003e\n\u003ch3\u003e2. Reduce the material cost of population and increase the utility benefit of returning population.\u003c/h3\u003e\n\u003cp\u003eWith the steady development of social economy and the significant improvement of people's quality of life, the daily consumption structure is gradually changing to diversified and refined. In addition to meeting the basic living expenses, the family income has become the main source of economic burden for ordinary families (Yang., 2019). In view of this, the government needs to take a series of targeted measures to effectively alleviate the economic pressure of families in this field. The government should focus on improving the quality and coverage of eugenics services. On the one hand, it is necessary to strengthen the construction of professional institutions and talent teams, especially the resource allocation and service capacity of maternal and child health departments of hospitals at all levels, so as to ensure that employees have professional qualifications and skills to meet the growing demand for maternal and child health care. At the same time, at the level of township and community, special maternal and child health service stations should be set up to form a service network covering urban and rural areas, ensure that the policy of eugenic and child-rearing is deeply rooted in the hearts of the people, and provide substantive support such as childcare allowance and tax reduction for highly educated talent families who have two or three children in response to the national policy. In terms of education cost control, the government needs to take a two-pronged approach, not only focusing on the improvement of education quality, but also reducing the economic burden of families.\u003c/p\u003e\n\u003ch3\u003e3. Increase financial support to shorten the income gap\u003c/h3\u003e\n\u003cp\u003eAccording to the explanation of labor economy, most of the reason for the large outflow of population is that the income from outflow is greater than that of Heilongjiang Province.The government needs to adopt proactive strategies through a series of policy tools and measures to guide and encourage talents to return to their hometowns to start businesses, and build a comprehensive and multi-level entrepreneurial support system for returning entrepreneurs, such as optimizing the entrepreneurial environment, providing site support, and simplifying the administrative approval process, so as to effectively alleviate the crowding-out effect that may be caused by the excessive concentration of government-led capital on returning entrepreneurs. Secondly, in terms of capital, the government should set up special entrepreneurial lending institutions and implement differentiated interest rate policies, especially for returning entrepreneurs, and provide more favorable loan conditions to reduce their financing costs and inject strong impetus into entrepreneurial activities. Establish and improve a more active tax policy, improve the individual tax system, reduce the tax burden of high-income groups by adjusting the personal income tax policy \u0026zwnj;, while reducing the amount of tax paid by low-income groups, and narrow the income gap.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJiyun Bai was responsible for conceptualization, methodology, funding acquisition, and final manuscript review and approval. Chengyu Yang contributed to the original draft preparation, data curation, formal analysis, and visualization. Xinyue Jin participated in methodology development and analysis and interpretation of data. Ying Cao contributed to manuscript review, editing, and formatting. All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that support the findings of this study are openly available from public sources. The population mobility data were obtained from Baidu Migration Big Data (https://qianxi.baidu.com/). The socioeconomic data were derived from the Heilongjiang Statistical Yearbook and China Statistical Yearbook, available from the National Bureau of Statistics of China (http://www.stats.gov.cn/). All data used in this study are publicly accessible as described.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCao Yang. Analysis on Strengthening strategies of Human resource management of rural unemployed [J]. 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Information and Control, 1995, 24(3): 162\u0026ndash;166.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"new quality productivity, Set-pair-social network analysis, Net population flow, Return flow drive","lastPublishedDoi":"10.21203/rs.3.rs-8877013/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8877013/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnder the background of accelerating the development of new quality productivity in China, population mobility, as a key factor, has become increasingly prominent in its spatial reorganization mechanism and regional differential effect. Based on Baidu migration big data and statistical yearbook data, this paper constructs a set pair-social network analysis method, optimizes social network data, enhances network characteristics, and comprehensively describes the network pattern of inter-provincial population mobility. Taking Heilongjiang Province of China as an example, this paper deeply analyzes the spatio-temporal evolution characteristics of population mobility and the driving mechanism of return flow of new quality productivity. The results show that the national population mobility network shows significant small-world characteristics and \"core-edge\" structure, and the regions with higher levels of new quality productivity occupy the hub position in the network. Heilongjiang Province is on the edge of the population flow network, with continuous outflow of population and highly uneven spatial distribution. The regression analysis shows that the new quality productivity has a significant negative impact on the overall population net flow in Heilongjiang Province, reflecting the mismatch between the development model of new quality productivity with technology intensive and low employment elasticity and the structure of local labor force. However, in cities with low population density, the new quality productivity has a significant role in promoting population return. The results show that the new quality productivity does not naturally have a population attraction effect, and its population effect highly depends on the matching degree between regional industry carrying capacity and population structure. This paper provides a new theoretical perspective and empirical basis for understanding the population mobility mechanism in developing regions and formulating differentiated population return policies.\u003c/p\u003e","manuscriptTitle":"Integrating set pair analysis and social network analysis to explore the distribution pattern and return flow mechanism of floating population: A case study of Heilongjiang Province, China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-17 14:39:03","doi":"10.21203/rs.3.rs-8877013/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-01T06:39:49+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-24T14:57:45+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-18T04:31:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"41421488352002643129596384058218249134","date":"2026-03-11T02:09:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"174219662916978040492430390057083866655","date":"2026-03-10T05:21:36+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-23T12:17:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-17T12:59:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-17T09:00:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Network Science","date":"2026-02-14T04:59:34+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"333c6fc6-760a-4d62-b0aa-4074e1575b90","owner":[],"postedDate":"February 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-16T02:23:12+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-17 14:39:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8877013","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8877013","identity":"rs-8877013","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}