Dynamic Interplay Between Internet Addiction and Anxiety Across Distinct Loneliness Trajectories in Adolescents: A Cross-Lagged Panel Network Analysis

Dynamic Interplay Between Internet Addiction and Anxiety Across Distinct Loneliness Trajectories in Adolescents: A Cross-Lagged Panel Network Analysis | 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 Dynamic Interplay Between Internet Addiction and Anxiety Across Distinct Loneliness Trajectories in Adolescents: A Cross-Lagged Panel Network Analysis Yuntai Wang, Zijuan Ma, Shiyi Lin, Guodong Gong, Xiaoyi Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7920077/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Purpose Loneliness is a prevalent psychological issue among adolescents. Anxiety and internet addiction (IA) are the most closely associated negative consequences of loneliness. Although prior research found a significant connection between the three, many of them overlooked individuals' distinct loneliness trajectories and their directional relationship at the symptom level. The purpose of this study was to identify complicated relationships and comorbidity models linking loneliness, anxiety, and IA across distinct trajectories of loneliness among adolescents. Methods The sample consisted of 1,720 adolescents from Yunnan, China, with data collected at two time points: T1 (October 2024) and T2 (March 2025). The UCLA Loneliness Scale (ULS), the Generalized Anxiety Disorder 7-item scale (GAD-7), and the Internet Addiction Test (IAT) were used to conduct the assessments. Cross-lagged panel network models were employed to investigate the various longitudinal associations between loneliness, anxiety, and IA symptoms over loneliness trajectories. Results Four distinct loneliness trajectories were identified: stable low, growing, decreasing, and stable high. The stable low trajectory was defined by 'Social isolation' (L1), the increasing trajectory by 'Nervousness' (A1), the decreasing trajectory by 'Worry too much' (A3), and the stable high trajectory by 'Excessive use' (I2). Loneliness sensations acted as bridge symptoms, connecting various elements of the network. Conclusion This innovative study demonstrates distinct loneliness trajectories and their bridging role in the comorbid network, providing vital insights for personalized mental health therapies to reduce loneliness, anxiety and IA. Adolescence Loneliness Internet Addiction Anxiety Network analysis Cross-lagged panel network design Figures Figure 1 Figure 2 Figure 3 1. Introduction Loneliness is defined as a painful feeling that occurs when there is an a gap between desired and real social interactions (Peplau & Perlman, 1982 ). In the digital age, loneliness has become a prominent psychological issue, particularly among adolescents (Christiansen et al., 2021 ). The Global School-Based Student Health Survey (GSHS), encompassing 70 nations, indicated that the global prevalence of loneliness among adolescents is 11.7% (95% CI: 10.6 to 12.7) (Global School-Based Student Health Survey, 2018). Due to physiological, psychological, and social role transformations in adolescence, the prevalence of loneliness varies markedly among age groups (Hang et al., 2023 ). A meta-analysis revealed that the prevalence of loneliness in adolescents (ages 12 to 17) was significantly higher compared to other age groups, varying from 9.2% (95% CI: 6.8 to 12.4%) in Southeast Asia to 14.4% (95% CI: 12.2 to 17.1%) in the Eastern Mediterranean region (Surkalim et al., 2022 ). Due to the pervasive and significant frequency of loneliness in teenagers, additional study is urgently needed to investigate the mechanisms of loneliness among adolescence. Nevertheless, current research mainly regards participants as a uniform cohort, giving inadequate attention to the distinct trajectories of loneliness among individuals. The first aim of this study is to analyze the distinct trajectories of loneliness in adolescents. In the digital era, the negative consequences of loneliness have become increasingly apparent. Loneliness intensifies several mental problems in teenagers, such as anxiety, depression, suicidal ideation, cognitive decline, and sleep disorders (Awn et al., 2023 ; Eres et al., 2021 ; Hernández et al., 2024 ; Hosozawa et al., 2022 ; Mufson & Rynn, 2019 ; Pearce et al., 2021 ; Tarabay et al., 2023 ). Among these issues, anxiety and Internet addiction (IA) are significantly associated with loneliness (Y. Wang & Ma, 2024 ; Y. Wang & Zeng, 2024 ; Yu et al., 2025 ). Research demonstrates that loneliness and anxiety often co-occur in teenagers and interact through intricate pathways (Danneel et al., 2020 ; Maes et al., 2019 ). Regarding Internet Addiction (IA), loneliness serves not only as a substantial predictor but may also signify a potential consequence of IA. Literature indicates that many investigations have not considered the internal correlation among loneliness, anxiety, and IA at the symptom level, frequently depending solely on total scores to analyze them, often lacking temporal data. Moreover, many research have neglected the distinct trajectories of loneliness, mainly focusing on the correlation between loneliness and a singular variable, thereby disregarding the intricate interactions among multiple variables. Therefore, the secondary aim of this study is to conceptualize the symptoms of loneliness, anxiety, and IA as a complex network and examine their dynamic variations across distinct trajectories of loneliness. 1.1 Loneliness and its trajectories Loneliness is prevalent among adolescents, and its distinct trajectories reveal considerable variation among individuals. These disparities may be affected by a confluence of genetic, environmental, social, and psychological factors (Hosozawa et al., 2022 ; Matthews et al., 2022 ). Loneliness symptoms may grow chronically, appear intensely, or diminish in a brief period (Nenov-Matt et al., 2020 ). Indeed, prior studies have verified the unique trajectories of loneliness during adolescence (Beattie et al., 2024 ; Chang et al., 2024 ; Hutten et al., 2021 ; Qualter et al., 2013 ). These trajectories not only indicate distinctive developmental patterns of loneliness in adolescence but are also strongly correlated with mental health consequences (Hosozawa et al., 2022 ). Previous research has emphasized the importance of creating heterogeneous comorbidity models that connect loneliness, anxiety, and IA across distinct trajectories of loneliness across adolescence. 1.2 The bidirectional relationships between loneliness, anxiety and IA 1.2.1 The bidirectional relationships between loneliness and anxiety Loneliness and anxiety tend to be intertwined in adolescence, an essential developmental phase. Empirical data reveals a high positive correlation between loneliness and anxiety symptoms in adolescents, with longitudinal research illustrating their reciprocal influences (Maes et al., 2019 ; O’Day & Heimberg, 2021 ). In a cohort of Kenyan adolescents, reported social isolation significantly predicted subsequent anxiety symptoms (Rodriguez et al., 2022 ). Increased loneliness not only exacerbates anxiety symptoms, but it may also enhance the experience of loneliness (Maes et al., 2019 ). The comorbidity of loneliness and anxiety may be due to adolescents' unique social-cognitive patterns, as lonely adolescents are more sensitive to negative social cues, which can exacerbate their social anxiety and reduce their anticipation of social interactions (Morningstar et al., 2019 ). 1.2.2 The bidirectional relationships between loneliness and IA With the extensive use of the Internet, adolescents' loneliness and IA are significantly associated. Data from Malaysian student samples demonstrate a notable correlation between loneliness and the incidence of IA (OR = 1.741, 95% CI: 1.084–2.794) (Zakaria et al., 2023 ). Teenage loneliness is associated with an increased incidence of IA and can potentially aggravate IA behavioral tendencies (Dong et al., 2023 ; Sarıalioğlu et al., 2022 ). On the other hand, IA can potentially exacerbate adolescent loneliness. While the Internet has enhanced social opportunities for adolescents in the digital age, research indicates that excessive engagement in online socialization may impair actual-life social skills, consequently intensifying feelings of loneliness (Sarıalioğlu et al., 2022 ; Tateno et al., 2019 ). 1.2.3 The bidirectional relationships between IA and anxiety . Anxiety, a prevalent mental disorder, has increasingly associated with IA. Numerous studies have identified anxiety as a significant predictor of IA. Studies indicate a significant positive correlation between anxiety and IA among teenagers across diverse age cohorts (Özbay et al., 2022 ; Stavropoulos et al., 2017 ). Also, IA may exacerbate anxiety symptoms (Dash et al., 2022 ; Xie et al., 2023 ). Excessive Internet use may result in decreased academic performance, social isolation, and reduced sleep quality, all of which can increase an individual's anxiety symptoms (Cai et al., 2021 ; Che et al., 2025 ). 1.3 Network analysis Conventional analytical methods based on total ratings are insufficient for revealing the relationships among symptoms. Recently, network analysis has become of growing popularity in mental health research, conceptualizing mental health disorders as interrelated symptom networks. Unlike previous approaches that treated mental disorders as "diseases" with clear etiological pathways (Borsboom, 2017 ), the network analysis perspective proposes that the origin of mental disorders is dappled, driven by mutual activation and dynamic development of symptoms (Borsboom & Cramer, 2013 ). In network analysis, mental disorders are depicted by network graphs, which generally have nodes and edges. Symptoms are depicted as nodes, with their relationships represented as edges. The nodes associated with various mental health disorders are divided into several communities (Epskamp et al., 2012 ). Identifying and treating in bridging symptoms can lead to cascading effects and improve treatment outcomes (Fried & Cramer, 2017 ). By depicting mental diseases as network graphs, network analysis helps uncover the most significant symptoms within the network and provide a clearer understanding of their dynamic relationships. Traditional cross-sectional studies cannot identify probable causal links between symptoms. The Cross-lagged Panel Network (CLPN) is a new approach for detecting autoregressive effects, cross-symptom lagged effects, and bridge centrality (Epskamp et al., 2012 ). By analyzing autoregressive effects and cross-lagged effects, the CLPN model can explain causal relationships between symptoms, identify symptoms with high out-Expected Influence (OEI) (strong predictive power for other symptoms), high in-Expected Influence (IEI) (easily predicted by other symptoms), and high bridge-Expected Influence (BEI) (key bridge symptoms across communities), thus providing targets for precise intervention (Epskamp et al., 2012 ; Fried & Cramer, 2017 ). This method is particularly useful for panel data with more than two time points, as it allows for the modeling of loneliness, anxiety, and IA symptoms and the examination of their dynamic changes throughout distinct loneliness trajectory. 1.4 The current study Existing research demonstrates that adolescent loneliness has distinct trajectories and bidirectional processes with anxiety and IA. Prior research, however, has three limitations: first, it treats the loneliness group as a homogeneous entity, ignoring its distinct trajectories; second, it relies on total score analyses and cross-sectional data, making it difficult to reveal dynamic associations among symptoms; and third, it lacks systematic modeling of multivariable comorbidity networks. To address these constraints, this study creatively blends trajectory analysis with network analysis approaches, employing the CLPN method to construct a dynamic comorbidity model of symptoms for loneliness, anxiety, and IA across distinct loneliness trajectories. Furthermore, by evaluating symptom centrality metrics across multiple loneliness trajectories, the study identifies primary and bridge symptoms of significant value. 2. Method 2.1 Participants This study employed a two-wave convenience sampling method to collect data from middle and high school students at a public school in Yunnan Province, China. The first wave was conducted in October 2024, with 2,181 students completing the assessment. The second wave took place in March 2025, with 1,889 students participating. Participants were categorized into classes, and each class filled out self-report questionnaires using paper-and-pencil methods in a classroom setting, supervised by two graduate students with expertise in applied psychology. Information collected from participants included age, gender (1 = male, 2 = female), ethnicity (1 = Han, 2 = ethnic minority), only child status (1 = yes, 2 = no), family residence (1 = urban, 2 = rural), and parents' marital status (1 = intact, 2 = divorced). After merging the two waves of data using the provided phone numbers, a total of 1,720 students submitted valid data regarding Internet addiction, loneliness, and anxiety symptoms, resulting in a valid response rate of 91.05%. Prior to the survey, all participants and their guardians signed informed consent forms, in which the participants were explicitly informed about the research objectives, assured that all data would be processed anonymously, and reminded of their rights to voluntary participation under the Declaration of Helsinki , including the right to withdraw at any time without penalty. Approval for the surveys was obtained from the local Education Bureau as well as from the principals of the participating schools. Furthermore, the research materials and procedures received ethical approval from the Scientific Review Group of the Applied Psychology Program, Faculty of Education, at our university. 2.2 Measures 2.2.1 UCLA Loneliness Scale (ULS) The UCLA Loneliness Scale, developed by D. Russell et al. ( 1980 ), assesses the level of loneliness through 20 items, each rated on a 4-point scale (1 = never, 4 = always). Previous research has identified three factors within the scale: Social Isolation (11 items), Social Relation Disconnectedness (5 items), and Social Collective Disconnectedness (4 items) (D. W. Russell, 1996 ). The Chinese version of the scale has demonstrated good reliability and validity among adolescents in Hong Kong (Ip et al., 2024 ). However, in this study, exploratory factor analysis revealed a different structure, comprising two factors: Social Isolation (11 items) and Social Disconnectedness (9 items). This deviation from the original structure may be attributed to the sample's collectivist cultural background, such as that of mainland China, where interpersonal connections are often formed within cohesive in-group communities (e.g., families, classrooms, and schools), complicating the distinction between relational and collective connections. Consequently, we adopted these two dimensions for our analysis. The Cronbach's α coefficients for this scale were satisfactory at both T1 ( α = 0.93) and T2 ( α = 0.92). 2.2.2 Internet Addiction Test (IAT) Kimberly Young's Internet Addiction Test (IAT) is among the most widely utilized diagnostic tools for assessing internet addiction (Faraci et al., 2013 ; Young, 1998 ). The Chinese version of this test has exhibited strong reliability and validity among Chinese adolescents (Lai et al., 2013 ). The IAT comprises 20 items categorized into 6 factors: Salience (5 items), Excessive Use (5 items), Neglect of Work (3 items), Anticipation (2 items), Lack of Control (3 items), and Neglect of Social Life (2 items), with each item rated on a 5-point Likert scale (Widyanto & McMurran, 2004 ). The Cronbach's α coefficients for this scale were satisfactory at T1 ( α = 0.92) and T2 ( α = 0.92). 2.2.3 General Anxiety Disorder (GAD-7) For the assessment of anxiety, this study employed the Chinese version of the 7-item Generalized Anxiety Disorder scale (GAD-7; Löwe et al., 2008 ), which ranges from 0 (not at all) to 3 (nearly every day). The GAD-7 has demonstrated strong reliability among Chinese adolescents (J. Wang et al., 2021 ), with Cronbach's α coefficients of 0.92 at T1 and 0.89 at T2, indicating adequate internal consistency. 2.3 Statistical analysis 2.3.1 Trajectories of loneliness symptoms Previous research has indicated that network models constructed based on groups defined by total scores do not introduce bias, whereas those based on general population samples may do so (Haslbeck et al., 2022 ). Therefore, we divided individuals into two groups—those experiencing loneliness and those not experiencing loneliness—using a total score cut-off point of 50 (D. W. Russell, 1996 ). Based on this cut-off score of the ULS, four loneliness trajectories were identified (Beattie et al., 2024 ; Chang et al., 2024 ; Hutten et al., 2021 ; Qualter et al., 2013 ): stable low, increasing, decreasing, and stable high. Specifically, the stable low group consisted of individuals whose ULS scores consistently remained below the cut-off value of 50. Participants in the decreasing group exhibited ULS scores above the threshold at T1 but below the threshold at T2. The increasing group consisted of individuals with ULS scores below the cut-off at T1 but above it at T2. 2.3.2 Network analysis All statistical analyses in this study were conducted using R (Version 4.4.2). To ensure uniform measurement, all symptom scores were transformed into z-scores prior to statistical analysis. The glmnet package was employed to compute regression and build a cross-lagged panel network (CLPN) model (Wysocki et al., 2017 ), utilizing LASSO (Least Absolute Shrinkage and Selection Operator) for sparse regularization to filter significant cross-temporal lag effects and reduce redundancy (Friedman et al., 2008). The regularization parameter λ was optimized through 10-fold cross-validation to balance model complexity with generalizability (Friedman et al., 2010 ). Additionally, based on the literature, we controlled for gender and age as covariates in the temporal networks (Barreto et al., 2021 ). The network structure was visualized using the qgraph package, where nodes signify symptoms, directed edges indicate cross-timepoint predictive effects, blue edges represent positive regression coefficients, and red edges denote negative regression coefficients. Edge thickness indicates the strength of the connection, while arrows represent the estimates of cross-lagged effects. To compute centrality indices and analyze directionality, the bootnet package was employed to estimate in-expected influence (IEI) and out-expected influence (OEI). A higher OEI value indicates that the symptom node at T1 exerts a stronger influence on all other symptom nodes at T2, while a higher IEI value suggests that the symptom node at T2 is more strongly affected by all other symptom nodes at T1. The 1-step bridge-expected influence (BEI) was utilized to identify bridge symptoms among IA, loneliness, and anxiety. In calculating BEI, only the edges between nodes and other communities were considered, excluding the edges connecting the node to its own community nodes (Jones et al., 2021). The ggplot2 package was employed to generate visual results. Key network metrics obtained, such as centrality metrics (e.g., edge, expected influence, bridge expected influence), were used to assess the strength of connections between nodes and the influence of individual nodes within the network, as well as the capacity of certain nodes to serve as bridges connecting other nodes. 2.3.3 Accuracy and Stability Estimation The bootnet package was utilized to validate the stability and accuracy of the network model (Epskamp et al., 2018 ). Initially, 1,000 bootstrap samples of the original data were drawn using non-parametric bootstrap methods to estimate the 95% confidence interval (CI) for edge weights, thereby assessing the network's stability. A broad CI derived from bootstrapping suggests challenges in ensuring edge stability. Subsequently, the case-drop bootstrap method was employed, which involves sequentially removing samples to evaluate the correlation stability coefficient (CS) and verify the accuracy of centrality measures. This coefficient represents the maximum proportion of cases that can be removed while preserving a correlation greater than 0.70 between the centrality metrics computed from the original network and the centrality index estimated from a new network that excludes the deleted cases. It is recommended that the CS coefficient exceed 0.25, with values above 0.50 indicating substantial robustness (Kim & Lee, 2022 ).. Moreover, the study further examined the presence of significant differences in centrality and edge weights, focusing specifically on the relational differences among Internet addiction, loneliness, and anxiety symptoms. The Non-parametric Bootstrap approach was employed to assess these differences in centrality and edge weights. The difference testing utilized the minimum confidence interval technique, with Bonferroni Correction applied to control for Type I error in multiple testing. Additionally, the differences in centrality and edge weights were visualized through a difference network and heat map, which were constructed to illustrate the variability and directionality of centrality metrics and edge weights. In the difference network, darker edge colors signify greater significance of the differences. 2.3.4 Network comparison We conducted a Kruskal-Wallis’s test to analyze the average edge weights of the communities across the four networks. When significant differences were identified through the Kruskal-Wallis’s test, post-hoc pairwise comparisons were performed using Dunn's test to determine which specific community pairs exhibited significant differences in edge weights. To control for Type I errors, a Bonferroni correction was applied. 3. Results 3.1 Demographic characteristics The gender distribution among participants was approximately balanced, with ages ranging from 11 to 20 years ( Mean ± SD = 14.46 ± 1.55). The majority of participants were of Han ethnicity, came from families with multiple children, were born in urban areas, and had parents with stable marital statuses. Additional demographic information is provided in Table 1 . Table 1 Demographic Information (N = 1720) Frequency Percentage Gender Male 882 51.28% Female 838 48.72% Age Junior adolescence (Age 14 and under) 1054 61.28% Senior adolescence (Age 15 and over) 666 38.72% Ethnic Han 1476 85.81% Minor 244 14.19% Family Fertility Only-child families 406 23.60% Multi-child families 1314 76.40% Birthplace Urban 1578 91.74% Rural 142 8.26% Parents' marriage Good 1594 92.67% Divorced 126 7.33% 3.2 Trajectories of loneliness symptoms Figure 1 illustrates four distinct trajectories of changes in loneliness symptoms: the stable low group, the increasing group, the decreasing group, and the stable high group. Out of 1,720 adolescents, 1,273 (74.01%) consistently scored below the critical threshold of 50 points on the UCLA Loneliness Scale (ULS), categorizing them into the stable low group. The increasing group, consisting of 60 adolescents (3.49%), had ULS scores below the critical threshold at T1 but exceeded the threshold at T2. The decreasing group, comprising 207 adolescents (12.03%), initially exhibited loneliness symptoms that gradually improved over time. Finally, adolescents who displayed positive loneliness symptoms at both time points were classified into the stable high group, which included 180 adolescents (10.47%). 3.3 Temporal networks across adolescence with distinct loneliness trajectories 3.3.1 Network stability and accuracy The accuracy plot reveals small to moderate confidence intervals surrounding the edge weights, suggesting that the CLPN model constructed from the four loneliness symptom trajectories demonstrates good accuracy (Supplementary Fig. S1 ). The results of case-drop bootstrapping indicate significant differences between the strongest and weakest edges (see Supplementary Fig. S2), thus affirming the accuracy of these edges (Epskamp & Fried, 2018 ). Furthermore, the case-dropping results (see Supplementary Fig. S3) show that the four groups of out-EI, in-EI, and bridge-EI exhibit at least small to moderate stability. The network models derived from the four loneliness trajectories present the following centrality stabilities coefficients (CSs) for out-EI, in-EI, and bridge-EI: for the stable low group: bridge-Expected Influence (CS = 0.75), in-Expected Influence (CS = 0.52), out-Expected Influence (CS = 0.60); for the increasing group: bridge-Expected Influence (CS = 0.75), in-Expected Influence (CS = 0.00), out-Expected Influence (CS = 0.05); for the decreasing group: bridge-Expected Influence (CS = 0.75), in-Expected Influence (CS = 0.13), out-Expected Influence (CS = 0.29); and for the stable high group: bridge-Expected Influence (CS = 0.75), in-Expected Influence (CS = 0.36), out-Expected Influence (CS = 0.36). The centrality difference tests for edge weight variations are illustrated in Supplementary Figs. S4, S5, and S6. 3.3.2 Network comparison Table 2 presents the findings from the Kruskal–Wallis analyses and the subsequent Dunn post-hoc tests, which examine the mean edge weights within each community. Significant differences in edge weights—both intra-community and inter-community—were observed among all trajectory group pairs, with the exception of the Increasing–Decreasing and Increasing–Stable High group pairs. Table 2 The Kruskal-Walli’s test and Dunn test results of average edge weights between and within each community (N = 1720). Community Stable-low Stable-High Increasing Decreasing p Significant pairs Loneliness 1.14 1 1 0.94 0.22 —— IA 1.09 1.14 1.07 1.08 0.82 —— Anxiety 1.05 1.09 1.17 1.08 0.01 Increasing - Stable-high** Increasing - Stable-low ** Loneliness → IA 1.03 1.01 0.99 0.98 < 0.00 Decreasing - Stable-high ** Decreasing - Stable-low*** Increasing - Stable-low *** Loneliness → Anxiety 1.07 0.99 0.99 0.98 < 0.00 Decreasing - Stable-low *** Increasing - Stable-low*** Stable-high - Stable-low *** Anxiety → Loneliness 1.01 1.01 1.02 0.99 0.11 —— Anxiety → IA 0.99 1.01 1.03 1 0.05 —— IA → Anxiety 1.01 1.02 0.99 1 0.01 Increasing - Stable-high ** IA → Loneliness 1 1.01 0.99 1.02 0.42 —— Note. *p < 0.05, **p < 0.01, ***p < 0.001 3.3.3 Cross-Lagged panel network models Figure 2 illustrates the cross-lagged panel network (CLPN) models corresponding to the four identified trajectories of loneliness symptoms. The detailed adjacency matrices for these networks are presented in supplementary Tables S1 through S4. To enhance the visual interpretability of the cross-lagged associations, autoregressive edges have been omitted from the primary network figures. Supplementary Fig. S7 offers an alternative network representation that includes both autoregressive and weaker edges. Figure 3 displays the network centrality metrics—out-Expected Influence, in-Expected Influence, and bridge-Expected Influence—while comprehensive results are available in Supplementary Table S5. Substantial differences in edge weights were observed both within and across communities in the four loneliness trajectory CLPN models. Within-community differences were noted in the context of Anxiety, while between-community differences were identified in the following relationships: IA → Anxiety, Loneliness → IA, and Loneliness → Anxiety, as detailed in Table 2 . Additionally, the most prominent within-community cross-lagged edges for the stable low, increasing, decreasing, and stable high groups were as follows: 'Anticipation' (I4) → 'Excessive use' (I2) (OR = 1.22), 'Trouble relaxing' (A4) → 'Nervousness' (A1) (OR = 0.38), 'Uncontrollable worrying' (A2) → 'Worry too much' (A3) (OR = 1.36), and 'Salience' (I1) → 'Excessive use' (I2) (OR = 1.50). The most significant between-community cross-lagged edges included: 'Uncontrollable worrying' (A2) → 'Social Isolation' (L1) (OR = 1.17), 'Neglect work' (I3) → 'Feeling afraid' (A7) (OR = 1.29), 'Anticipation' (I4) → 'Uncontrollable worrying' (A2) (OR = 0.82), and 'Restlessness' (A5) → 'Excessive use' (I2) (OR = 1.20). 3.3.4 Network inference The results of the network centrality metrics are illustrated in Fig. 3 . In the stable low group, 'Social Isolation' (L1) exhibited the highest out-Expected Influence (OEI = 2.48). In the increasing group, 'Nervousness' (A1) showed the highest out-EI (OEI = 1.60). In the decreasing group, 'Worry too much' (A3) had the highest out-EI (OEI = 2.34). Finally, in the stable high group, 'Excessive use' (I2) demonstrated the highest out-EI (OEI = 2.70), indicating its strong predictive power over other symptoms within the network structure. In the stable low group, 'Uncontrollable worrying' (A2) exhibited the highest in-Expected Influence (IEI = 1.63). In the increasing group, 'Restlessness' (A5) displayed the highest in-EI (IEI = 1.37). In the decreasing group, 'Excessive use' (I2) had the highest in-EI (IEI = 1.43). In the stable high group, 'Salience' (I1) had the highest in-EI (IEI = 1.76), suggesting a strong vulnerability to the influence of other symptoms within the network. Furthermore, loneliness symptoms exhibited the highest bridge-Expected Influence (BEI) across all groups: in the stable low group (BEI = 2.60 (L1), BEI = 2.11 (L2)); in the increasing group (BEI = 2.26 (L1), BEI = 2.46 (L2)); in the decreasing group (BEI = 2.38 (L1), BEI = 2.28 (L2)); and in the stable high group (BEI = 2.35 (L1), BEI = 2.31 (L2)). 4. Discussion This study conducts network modeling using longitudinal data from a large adolescent cohort, making it the first to demonstrate unique longitudinal correlations between loneliness, anxiety and IA across distinct trajectories of loneliness symptoms. Three main findings were identified: The structure of symptom networks related to loneliness, anxiety and IA differed across various trajectories of loneliness. Secondly, within the comorbidity networks, 'Social Isolation' (L1) in the stable low trajectory, 'Nervousness' (A1) in the increasing trajectory, 'Worry too much' (A3) in the decreasing trajectory, and 'Excessive use' (I2) in the stable high trajectory were identified as the most significant predictors of other symptoms. Third, 'Social Isolation' (L1) and 'Social Disconnectedness' (L2) were identified as the most prominent bridge symptoms in the comorbidity networks of all four loneliness trajectories. Trajectory analysis identified four distinct developmental patterns of loneliness in Chinese adolescents: stable low (n = 1273, 74.01%), increasing (n = 60, 3.49%), decreasing (n = 207, 12.03%), and stable high (n = 180, 10.47%). The observed patterns correspond to the trajectory groupings identified in previous studies (Beattie et al., 2024 ; Chang et al., 2024 ; Hutten et al., 2021 ; Qualter et al., 2013 ). The distribution of participants among these trajectory groups did not fully align with prior findings. The increasing group constituted a larger proportion than previously reported, whereas both the decreasing and stable high groups were underrepresented compared to earlier studies (increasing: 37%; decreasing: 23%; stable high: 22%). The discrepancy between our findings and previous reports is most likely due to differences in assessment instruments, temporal measurement intervals, and cultural context (Olson et al., 2022 ). The trajectory analysis shows that, despite the majority of teens appear to be free of significant loneliness, a significant portion continues to experience either increasing or stable high levels. This emphasizes the significance of constant surveillance and intervention efforts to combat loneliness and related disorders. In the directed network model of the stable-low group identifies 'Social Isolation' (L1) as a strong predictor of IA and anxiety symptoms. This finding is consistent with previous research, shown that social isolation is a key component in the onset and prediction of IA and anxiety symptoms, even in groups with relatively low levels of loneliness (Liang et al., 2023 ). The comorbidity between loneliness and social anxiety is especially prominent in adolescents, with growing levels of loneliness aggravate social anxiety symptoms. The development of social anxiety can exacerbate feelings of loneliness, consequently perpetuating a negative feedback loop (Eres et al., 2023 ). Loneliness has been recognized as a significant risk factor for IA within the realm of digital interaction (Saadati et al., 2021 ). Likewise, neuroscience research aligns with our study. Research has identified an abnormal correlation between social isolation and the functioning of the Default Mode Network (DMN), perhaps leading individuals to experience discomfort in genuine social interactions, so driving them to find refuge in the virtual realm, consequently heightening the risk of IA (Cerniglia et al., 2017 ; Reed et al., 2015 ). Moreover, social isolation is intricately associated with the heightened activation of the hypothalamic-pituitary-adrenal (HPA) axis, leading to increased cortisol levels that intensify anxiety symptoms (Kubo et al., 2022 ; Reed et al., 2015 ). According to the Model of Compensatory Use, people may turn to virtual sociability to cope with actual loneliness, while this emotional isolation can lead to online addiction (Cauberghe et al., 2021 ). This proactive engagement with the internet may unconsciously increase anxiety levels, creating an undesirable cycle (Hernández et al., 2024 ). In the Increasing group, the symptom of 'Nervousness' (A1) within the anxiety community demonstrates the highest OEI, indicating that anxiety symptoms may significantly predict the rise of loneliness among adolescents. According to research, an increase of anxiety symptoms significantly boosts feelings of loneliness, especially in adolescents with deteriorating social connections (Campagne, 2019 ; Nguyen et al., 2024 ). Furthermore, it is important to note that the interaction between anxiety and loneliness, as well as internet addiction behaviors, is bidirectional; loneliness and internet addiction can increase anxiety symptoms, leading to a vicious cycle (Hernández et al., 2024 ). Cognitive Behavioral Therapy (CBT) aimed at addressing adolescent-specific anxiety symptoms, along with mindfulness-based therapies, may prove to be advantageous approaches for reducing the increasing severity of loneliness in adolescents (Goldin et al., 2021 ). In the symptom network of the decreasing group of adolescent loneliness, the anxiety symptom 'Worry too much' (A3) had the most predictive influence on loneliness, IA, and anxiety symptoms. 'Worry too much', a core symptom of anxiety disorders (Fico et al., 2023 ),, directly exacerbates anxiety symptoms and, through complex psychological mechanisms, contributes to the growth of loneliness and IA. According to O'Connor et al. (2023), adolescents with higher levels of loneliness are more likely to worry excessively about future uncertainty, which can worsen their anxiety symptoms (O’Connor et al., 2023 ). Adolescents who worry excessively are more likely to seek emotional and social assistance online in order to cope with stress and uncertainty (Cauberghe et al., 2021 ). Effective interventions addressing 'Worry too much' (A3) and related anxiety symptoms may reduce loneliness and hence improve teenagers' psychological well-being. In the symptom network structure of the stable-high loneliness group among adolescents, the symptom of 'Excessive use' (I2) associated with IA had the strongest predictive effect on loneliness, IA, and anxiety symptoms. This highlights that IA may significantly contribute to the constant feeling of loneliness. This study's findings reveal that the primary symptom of IA is 'Excessive use' (I2), which is consistent with previous research (Sha et al., 2019 ). Over time, 'Excessive use' (I2) heightens the individual's demand for internet use, resulting in increased tolerance, which in turn sustains and worsens symptoms of internet addiction (Tiego et al., 2019 ). The continuous dependence of adolescents on the internet may mitigate feelings of loneliness and anxiety (Hernández et al., 2024 ). However, this type of escapism impairs their ability to face real-life issues, resulting in a vicious loop (Tadpatrikar et al., 2024 ).. Interestingly, we found that in the four loneliness trajectory groups, the Indices of in-Expected Influence (IEIs) for the bridge symptoms 'Social Isolation' (L1) and 'Social Disconnectedness' (L2) were both less than one (Supplementary Fig. S2). This finding indicates that loneliness is negatively correlated with other symptoms. Loneliness symptoms may be alleviated or diminished under specific circumstances. Adolescents who experience loneliness may seek social support online and engage in self-soothing behaviors (Cauberghe et al., 2021 ). However, this positive aim may not be beneficial in the long term, and as proven by our study findings, it may exacerbate the chronic and complexities of loneliness. Our findings suggest that whether loneliness causes distress or exacerbates the complexity of mental disorder treatments and psychological issues, loneliness (particularly social isolation) as a transdiagnostic factor should be a key focus for preventive interventions aimed at IA and anxiety. 5. Limitation and future research Despite its novel investigation of the relationship between IA, loneliness, and anxiety symptoms across distinct loneliness trajectories among adolescents, this study has certain limitations. First, the two-wave design limits the ability to notice subtle shifts in symptoms and prevents tracking their dynamic changes with exquisite temporal resolution. Future research may integrate ecological momentary assessment (EMA) with longitudinal methods, facilitating more accurate and regular monitoring of symptom variations and their interconnections. Second, the study was conducted solely with a non-clinical sample. While it provides basic information about the links between IA, loneliness, and anxiety symptoms in the general population, the diversity of mental diseases needs future expansion to clinical groups. Third, the study focused on Chinese adolescents; while the findings capture key elements of this population, their ecological validity is limited due to reliance on a single cultural background. Future research should expand its focus to encompass samples from varied cultural and cross-national populations to assess the generalizability and applicability of the results. Fourth, the trajectory groups demonstrated low centrality indices (out-EI, in-EI), warranting careful interpretation(Epskamp, S. et al., 2018 ). In conclusion, the CLPN approach is restricted to proposing potential causal relationships; therefore, further experimental research is necessary to validate these findings. 6. Conclusion This study presents the first evidence of significant difference in the network structure of symptoms linked to loneliness, anxiety and IA across different loneliness trajectories in teenagers, highlighting the diversity of loneliness and its accompanying mental issues. Furthermore, the data show that 'Social Isolation' (L1), 'Nervousness' (A1), 'Worry too much' (A3), and 'Excessive usage' (I2) are key symptoms in the different trajectories of loneliness development. Finally, our findings show that loneliness symptoms act as a connection in the comorbid network of IA and anxiety, connecting multiple mental health issues. The findings of this study establish theoretical basis for the development of more comprehensive effective intervention strategies targeted at enhancing adolescent mental health and overall well-being. Declarations Author Contribution Yuntai Wang conceived the study, designed the study, performed the statistical analysis, interpreted the data, coordinated, and drafted the manuscript; Zijuan Ma helped to design the study and drafted the manuscript; Shiyi Lin interpreted the data, performed the statistical analysis, and conducted the measurements; Guodong Gong interpreted the data, performed the statistical analysis, and conducted the measurements; and Xiaoyi Huang interpreted the data and performed the measurements. All authors reviewed the manuscript. Acknowledgement None. References Awn MA, Mohroofi AD, Alsaqer JK, Aljowder AA, Mohroofi AD, Alsuliti MA (2023) Impact of covid-19 outbreak on the behavior of children and adolescents in the Kingdom of Bahrain. Medicine 102(45):e35925. https://doi.org/10.1097/md.0000000000035925 Barreto M, Victor C, Hammond C, Eccles A, Richins MT, Qualter P (2021) Loneliness around the world: Age, gender, and cultural differences in loneliness. 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06:50:23","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33465,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/a1ec1e0f3c465ddbf3cd1630.png"},{"id":94816237,"identity":"c82c0daa-479f-4976-af99-508766ffea46","added_by":"auto","created_at":"2025-10-31 04:42:10","extension":"xml","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":206321,"visible":true,"origin":"","legend":"","description":"","filename":"1d7084be30ea4265b52a340b17c482611structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/4d7959466f62a60edc7db015.xml"},{"id":94816238,"identity":"bb4975d1-680d-41e7-b8f3-d68f79958fdf","added_by":"auto","created_at":"2025-10-31 04:42:10","extension":"html","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":213964,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/14163088e3d39e99f06b561c.html"},{"id":94816217,"identity":"7493ddb9-07d0-48aa-b6db-76ea99973853","added_by":"auto","created_at":"2025-10-31 04:42:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":47016,"visible":true,"origin":"","legend":"\u003cp\u003eThe four trajectories of loneliness symptoms from T1to T2 among adolescence. (N=1720)\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/aeff7d56ff6d14565484500c.png"},{"id":94816215,"identity":"00ee8221-7f7d-43e7-8944-69be6c773efb","added_by":"auto","created_at":"2025-10-31 04:42:09","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":94709,"visible":true,"origin":"","legend":"\u003cp\u003eCross-lagged panel network of Internet addiction, loneliness, and anxiety symptoms from 2024 to 2025. Blue edges represent positive correlations (i.e., odds ratios greater than 1), and red edges represent negative correlations (i.e., odds ratios less than 1) The thickness of the edges represents the strength of OR, with thicker edges indicating stronger relationships. For visual clarity, the autoregressive edges are hidden\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNote. \u003c/strong\u003eA1=Nervousness, A2=Uncontrollable worrying, A3=Worry too much, A4=Trouble relaxing, A5=Restlessness, A6=Irritability, A7=Feeling afraid, I1=Salience, I2=Excessive use, I3=Neglect work, I4=Anticipation, I5=Lack of control, I6=Neglect social life, L1=Social Isolation, L2=Social Disconnectedness.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/e35f14b35e3885e8d6705b03.jpeg"},{"id":94816219,"identity":"65449753-8bd1-488a-9ce6-b9fe8ffc2996","added_by":"auto","created_at":"2025-10-31 04:42:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":177248,"visible":true,"origin":"","legend":"\u003cp\u003eCentrality estimates across four trajectories of loneliness symptoms (\u003cem\u003ez\u003c/em\u003e values)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNote. \u003c/strong\u003eHigh values indicate more centrality. A1=Nervousness, A2=Uncontrollable worrying, A3=Worry too much, A4=Trouble relaxing, A5=Restlessness, A6=Irritability, A7=Feeling afraid, I1=Salience, I2=Excessive use, I3=Neglect work, I4=Anticipation, I5=Lack of control, I6=Neglect social life, L1=Social Isolation, L2=Social Disconnectedness.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/bf16d06b73eabc0b9abd617f.png"},{"id":97135425,"identity":"37154319-52de-4e62-b8eb-09d9fbcba681","added_by":"auto","created_at":"2025-12-01 09:44:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1336358,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/ce99b19b-faa3-4830-b9fe-4dffa86d6bfe.pdf"},{"id":94816220,"identity":"3cc87834-956f-426c-a036-6fde7cd1faef","added_by":"auto","created_at":"2025-10-31 04:42:09","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":965203,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-7920077/v1/68e6972cb32cbbb763e6031e.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic Interplay Between Internet Addiction and Anxiety Across Distinct Loneliness Trajectories in Adolescents: A Cross-Lagged Panel Network Analysis","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLoneliness is defined as a painful feeling that occurs when there is an a gap between desired and real social interactions (Peplau \u0026amp; Perlman, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1982\u003c/span\u003e). In the digital age, loneliness has become a prominent psychological issue, particularly among adolescents (Christiansen et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The Global School-Based Student Health Survey (GSHS), encompassing 70 nations, indicated that the global prevalence of loneliness among adolescents is 11.7% (95% CI: 10.6 to 12.7) (Global School-Based Student Health Survey, 2018). Due to physiological, psychological, and social role transformations in adolescence, the prevalence of loneliness varies markedly among age groups (Hang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A meta-analysis revealed that the prevalence of loneliness in adolescents (ages 12 to 17) was significantly higher compared to other age groups, varying from 9.2% (95% CI: 6.8 to 12.4%) in Southeast Asia to 14.4% (95% CI: 12.2 to 17.1%) in the Eastern Mediterranean region (Surkalim et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Due to the pervasive and significant frequency of loneliness in teenagers, additional study is urgently needed to investigate the mechanisms of loneliness among adolescence. Nevertheless, current research mainly regards participants as a uniform cohort, giving inadequate attention to the distinct trajectories of loneliness among individuals. The first aim of this study is to analyze the distinct trajectories of loneliness in adolescents.\u003c/p\u003e\u003cp\u003eIn the digital era, the negative consequences of loneliness have become increasingly apparent. Loneliness intensifies several mental problems in teenagers, such as anxiety, depression, suicidal ideation, cognitive decline, and sleep disorders (Awn et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Eres et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hern\u0026aacute;ndez et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hosozawa et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Mufson \u0026amp; Rynn, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Pearce et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Tarabay et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Among these issues, anxiety and Internet addiction (IA) are significantly associated with loneliness (Y. Wang \u0026amp; Ma, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Y. Wang \u0026amp; Zeng, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Yu et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Research demonstrates that loneliness and anxiety often co-occur in teenagers and interact through intricate pathways (Danneel et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Maes et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Regarding Internet Addiction (IA), loneliness serves not only as a substantial predictor but may also signify a potential consequence of IA. Literature indicates that many investigations have not considered the internal correlation among loneliness, anxiety, and IA at the symptom level, frequently depending solely on total scores to analyze them, often lacking temporal data. Moreover, many research have neglected the distinct trajectories of loneliness, mainly focusing on the correlation between loneliness and a singular variable, thereby disregarding the intricate interactions among multiple variables. Therefore, the secondary aim of this study is to conceptualize the symptoms of loneliness, anxiety, and IA as a complex network and examine their dynamic variations across distinct trajectories of loneliness.\u003c/p\u003e\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e1.1 Loneliness and its trajectories\u003c/h2\u003e\u003cp\u003eLoneliness is prevalent among adolescents, and its distinct trajectories reveal considerable variation among individuals. These disparities may be affected by a confluence of genetic, environmental, social, and psychological factors (Hosozawa et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Matthews et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Loneliness symptoms may grow chronically, appear intensely, or diminish in a brief period (Nenov-Matt et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Indeed, prior studies have verified the unique trajectories of loneliness during adolescence (Beattie et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chang et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hutten et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Qualter et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). These trajectories not only indicate distinctive developmental patterns of loneliness in adolescence but are also strongly correlated with mental health consequences (Hosozawa et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Previous research has emphasized the importance of creating heterogeneous comorbidity models that connect loneliness, anxiety, and IA across distinct trajectories of loneliness across adolescence.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e1.2 The bidirectional relationships between loneliness, anxiety and IA\u003c/h2\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003e1.2.1 The bidirectional relationships between loneliness and anxiety\u003c/h2\u003e\u003cp\u003eLoneliness and anxiety tend to be intertwined in adolescence, an essential developmental phase. Empirical data reveals a high positive correlation between loneliness and anxiety symptoms in adolescents, with longitudinal research illustrating their reciprocal influences (Maes et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; O\u0026rsquo;Day \u0026amp; Heimberg, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In a cohort of Kenyan adolescents, reported social isolation significantly predicted subsequent anxiety symptoms (Rodriguez et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Increased loneliness not only exacerbates anxiety symptoms, but it may also enhance the experience of loneliness (Maes et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The comorbidity of loneliness and anxiety may be due to adolescents' unique social-cognitive patterns, as lonely adolescents are more sensitive to negative social cues, which can exacerbate their social anxiety and reduce their anticipation of social interactions (Morningstar et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e1.2.2 The bidirectional relationships between loneliness and IA\u003c/h2\u003e\u003cp\u003eWith the extensive use of the Internet, adolescents' loneliness and IA are significantly associated. Data from Malaysian student samples demonstrate a notable correlation between loneliness and the incidence of IA (OR\u0026thinsp;=\u0026thinsp;1.741, 95% CI: 1.084\u0026ndash;2.794) (Zakaria et al., \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Teenage loneliness is associated with an increased incidence of IA and can potentially aggravate IA behavioral tendencies (Dong et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sarıalioğlu et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). On the other hand, IA can potentially exacerbate adolescent loneliness. While the Internet has enhanced social opportunities for adolescents in the digital age, research indicates that excessive engagement in online socialization may impair actual-life social skills, consequently intensifying feelings of loneliness (Sarıalioğlu et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Tateno et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e\u003cb\u003e1.2.3 The bidirectional relationships between IA and anxiety\u003c/b\u003e.\u003c/h2\u003e\u003cp\u003eAnxiety, a prevalent mental disorder, has increasingly associated with IA. Numerous studies have identified anxiety as a significant predictor of IA. Studies indicate a significant positive correlation between anxiety and IA among teenagers across diverse age cohorts (\u0026Ouml;zbay et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Stavropoulos et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Also, IA may exacerbate anxiety symptoms (Dash et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Xie et al., \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Excessive Internet use may result in decreased academic performance, social isolation, and reduced sleep quality, all of which can increase an individual's anxiety symptoms (Cai et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Che et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e1.3 Network analysis\u003c/h2\u003e\u003cp\u003eConventional analytical methods based on total ratings are insufficient for revealing the relationships among symptoms. Recently, network analysis has become of growing popularity in mental health research, conceptualizing mental health disorders as interrelated symptom networks. Unlike previous approaches that treated mental disorders as \"diseases\" with clear etiological pathways (Borsboom, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), the network analysis perspective proposes that the origin of mental disorders is dappled, driven by mutual activation and dynamic development of symptoms (Borsboom \u0026amp; Cramer, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). In network analysis, mental disorders are depicted by network graphs, which generally have nodes and edges. Symptoms are depicted as nodes, with their relationships represented as edges. The nodes associated with various mental health disorders are divided into several communities (Epskamp et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Identifying and treating in bridging symptoms can lead to cascading effects and improve treatment outcomes (Fried \u0026amp; Cramer, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). By depicting mental diseases as network graphs, network analysis helps uncover the most significant symptoms within the network and provide a clearer understanding of their dynamic relationships.\u003c/p\u003e\u003cp\u003eTraditional cross-sectional studies cannot identify probable causal links between symptoms. The Cross-lagged Panel Network (CLPN) is a new approach for detecting autoregressive effects, cross-symptom lagged effects, and bridge centrality (Epskamp et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). By analyzing autoregressive effects and cross-lagged effects, the CLPN model can explain causal relationships between symptoms, identify symptoms with high out-Expected Influence (OEI) (strong predictive power for other symptoms), high in-Expected Influence (IEI) (easily predicted by other symptoms), and high bridge-Expected Influence (BEI) (key bridge symptoms across communities), thus providing targets for precise intervention (Epskamp et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Fried \u0026amp; Cramer, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This method is particularly useful for panel data with more than two time points, as it allows for the modeling of loneliness, anxiety, and IA symptoms and the examination of their dynamic changes throughout distinct loneliness trajectory.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e1.4 The current study\u003c/h2\u003e\u003cp\u003eExisting research demonstrates that adolescent loneliness has distinct trajectories and bidirectional processes with anxiety and IA. Prior research, however, has three limitations: first, it treats the loneliness group as a homogeneous entity, ignoring its distinct trajectories; second, it relies on total score analyses and cross-sectional data, making it difficult to reveal dynamic associations among symptoms; and third, it lacks systematic modeling of multivariable comorbidity networks. To address these constraints, this study creatively blends trajectory analysis with network analysis approaches, employing the CLPN method to construct a dynamic comorbidity model of symptoms for loneliness, anxiety, and IA across distinct loneliness trajectories. Furthermore, by evaluating symptom centrality metrics across multiple loneliness trajectories, the study identifies primary and bridge symptoms of significant value.\u003c/p\u003e\u003c/div\u003e"},{"header":"2. Method","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Participants\u003c/h2\u003e\u003cp\u003eThis study employed a two-wave convenience sampling method to collect data from middle and high school students at a public school in Yunnan Province, China. The first wave was conducted in October 2024, with 2,181 students completing the assessment. The second wave took place in March 2025, with 1,889 students participating. Participants were categorized into classes, and each class filled out self-report questionnaires using paper-and-pencil methods in a classroom setting, supervised by two graduate students with expertise in applied psychology. Information collected from participants included age, gender (1\u0026thinsp;=\u0026thinsp;male, 2\u0026thinsp;=\u0026thinsp;female), ethnicity (1\u0026thinsp;=\u0026thinsp;Han, 2\u0026thinsp;=\u0026thinsp;ethnic minority), only child status (1\u0026thinsp;=\u0026thinsp;yes, 2\u0026thinsp;=\u0026thinsp;no), family residence (1\u0026thinsp;=\u0026thinsp;urban, 2\u0026thinsp;=\u0026thinsp;rural), and parents' marital status (1\u0026thinsp;=\u0026thinsp;intact, 2\u0026thinsp;=\u0026thinsp;divorced).\u003c/p\u003e\u003cp\u003eAfter merging the two waves of data using the provided phone numbers, a total of 1,720 students submitted valid data regarding Internet addiction, loneliness, and anxiety symptoms, resulting in a valid response rate of 91.05%. Prior to the survey, all participants and their guardians signed informed consent forms, in which the participants were explicitly informed about the research objectives, assured that all data would be processed anonymously, and reminded of their rights to voluntary participation under the \u003cem\u003eDeclaration of Helsinki\u003c/em\u003e, including the right to withdraw at any time without penalty. Approval for the surveys was obtained from the local Education Bureau as well as from the principals of the participating schools. Furthermore, the research materials and procedures received ethical approval from the Scientific Review Group of the Applied Psychology Program, Faculty of Education, at our university.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Measures\u003c/h2\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1 UCLA Loneliness Scale (ULS)\u003c/h2\u003e\u003cp\u003eThe UCLA Loneliness Scale, developed by D. Russell et al. (\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e1980\u003c/span\u003e), assesses the level of loneliness through 20 items, each rated on a 4-point scale (1\u0026thinsp;=\u0026thinsp;never, 4\u0026thinsp;=\u0026thinsp;always). Previous research has identified three factors within the scale: Social Isolation (11 items), Social Relation Disconnectedness (5 items), and Social Collective Disconnectedness (4 items) (D. W. Russell, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). The Chinese version of the scale has demonstrated good reliability and validity among adolescents in Hong Kong (Ip et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, in this study, exploratory factor analysis revealed a different structure, comprising two factors: Social Isolation (11 items) and Social Disconnectedness (9 items). This deviation from the original structure may be attributed to the sample's collectivist cultural background, such as that of mainland China, where interpersonal connections are often formed within cohesive in-group communities (e.g., families, classrooms, and schools), complicating the distinction between relational and collective connections. Consequently, we adopted these two dimensions for our analysis. The Cronbach's \u003cem\u003eα\u003c/em\u003e coefficients for this scale were satisfactory at both T1 (\u003cem\u003eα\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.93) and T2 (\u003cem\u003eα\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.92).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003e2.2.2 Internet Addiction Test (IAT)\u003c/h2\u003e\u003cp\u003eKimberly Young's Internet Addiction Test (IAT) is among the most widely utilized diagnostic tools for assessing internet addiction (Faraci et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Young, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). The Chinese version of this test has exhibited strong reliability and validity among Chinese adolescents (Lai et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The IAT comprises 20 items categorized into 6 factors: Salience (5 items), Excessive Use (5 items), Neglect of Work (3 items), Anticipation (2 items), Lack of Control (3 items), and Neglect of Social Life (2 items), with each item rated on a 5-point Likert scale (Widyanto \u0026amp; McMurran, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). The Cronbach's \u003cem\u003eα\u003c/em\u003e coefficients for this scale were satisfactory at T1 (\u003cem\u003eα\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.92) and T2 (\u003cem\u003eα\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.92).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003ch2\u003e2.2.3 General Anxiety Disorder (GAD-7)\u003c/h2\u003e\u003cp\u003eFor the assessment of anxiety, this study employed the Chinese version of the 7-item Generalized Anxiety Disorder scale (GAD-7; L\u0026ouml;we et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), which ranges from 0 (not at all) to 3 (nearly every day). The GAD-7 has demonstrated strong reliability among Chinese adolescents (J. Wang et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), with Cronbach's \u003cem\u003eα\u003c/em\u003e coefficients of 0.92 at T1 and 0.89 at T2, indicating adequate internal consistency.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Statistical analysis\u003c/h2\u003e\u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1 Trajectories of loneliness symptoms\u003c/h2\u003e\u003cp\u003ePrevious research has indicated that network models constructed based on groups defined by total scores do not introduce bias, whereas those based on general population samples may do so (Haslbeck et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Therefore, we divided individuals into two groups\u0026mdash;those experiencing loneliness and those not experiencing loneliness\u0026mdash;using a total score cut-off point of 50 (D. W. Russell, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). Based on this cut-off score of the ULS, four loneliness trajectories were identified (Beattie et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chang et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hutten et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Qualter et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e): stable low, increasing, decreasing, and stable high. Specifically, the stable low group consisted of individuals whose ULS scores consistently remained below the cut-off value of 50. Participants in the decreasing group exhibited ULS scores above the threshold at T1 but below the threshold at T2. The increasing group consisted of individuals with ULS scores below the cut-off at T1 but above it at T2.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e2.3.2 Network analysis\u003c/h2\u003e\u003cp\u003eAll statistical analyses in this study were conducted using R (Version 4.4.2). To ensure uniform measurement, all symptom scores were transformed into z-scores prior to statistical analysis. The \u003cem\u003eglmnet\u003c/em\u003e package was employed to compute regression and build a cross-lagged panel network (CLPN) model (Wysocki et al., \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), utilizing LASSO (Least Absolute Shrinkage and Selection Operator) for sparse regularization to filter significant cross-temporal lag effects and reduce redundancy (Friedman et al., 2008). The regularization parameter \u003cem\u003eλ\u003c/em\u003e was optimized through 10-fold cross-validation to balance model complexity with generalizability (Friedman et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Additionally, based on the literature, we controlled for gender and age as covariates in the temporal networks (Barreto et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The network structure was visualized using the \u003cem\u003eqgraph\u003c/em\u003e package, where nodes signify symptoms, directed edges indicate cross-timepoint predictive effects, blue edges represent positive regression coefficients, and red edges denote negative regression coefficients. Edge thickness indicates the strength of the connection, while arrows represent the estimates of cross-lagged effects.\u003c/p\u003e\u003cp\u003eTo compute centrality indices and analyze directionality, the \u003cem\u003ebootnet\u003c/em\u003e package was employed to estimate in-expected influence (IEI) and out-expected influence (OEI). A higher OEI value indicates that the symptom node at T1 exerts a stronger influence on all other symptom nodes at T2, while a higher IEI value suggests that the symptom node at T2 is more strongly affected by all other symptom nodes at T1. The 1-step bridge-expected influence (BEI) was utilized to identify bridge symptoms among IA, loneliness, and anxiety. In calculating BEI, only the edges between nodes and other communities were considered, excluding the edges connecting the node to its own community nodes (Jones et al., 2021). The \u003cem\u003eggplot2\u003c/em\u003e package was employed to generate visual results. Key network metrics obtained, such as centrality metrics (e.g., edge, expected influence, bridge expected influence), were used to assess the strength of connections between nodes and the influence of individual nodes within the network, as well as the capacity of certain nodes to serve as bridges connecting other nodes.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\u003ch2\u003e2.3.3 Accuracy and Stability Estimation\u003c/h2\u003e\u003cp\u003eThe \u003cem\u003ebootnet\u003c/em\u003e package was utilized to validate the stability and accuracy of the network model (Epskamp et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Initially, 1,000 bootstrap samples of the original data were drawn using non-parametric bootstrap methods to estimate the 95% confidence interval (CI) for edge weights, thereby assessing the network's stability. A broad CI derived from bootstrapping suggests challenges in ensuring edge stability. Subsequently, the case-drop bootstrap method was employed, which involves sequentially removing samples to evaluate the correlation stability coefficient (CS) and verify the accuracy of centrality measures. This coefficient represents the maximum proportion of cases that can be removed while preserving a correlation greater than 0.70 between the centrality metrics computed from the original network and the centrality index estimated from a new network that excludes the deleted cases. It is recommended that the CS coefficient exceed 0.25, with values above 0.50 indicating substantial robustness (Kim \u0026amp; Lee, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)..\u003c/p\u003e\u003cp\u003eMoreover, the study further examined the presence of significant differences in centrality and edge weights, focusing specifically on the relational differences among Internet addiction, loneliness, and anxiety symptoms. The \u003cem\u003eNon-parametric Bootstrap\u003c/em\u003e approach was employed to assess these differences in centrality and edge weights. The difference testing utilized the minimum confidence interval technique, with \u003cem\u003eBonferroni Correction\u003c/em\u003e applied to control for Type I error in multiple testing. Additionally, the differences in centrality and edge weights were visualized through a difference network and heat map, which were constructed to illustrate the variability and directionality of centrality metrics and edge weights. In the difference network, darker edge colors signify greater significance of the differences.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\u003ch2\u003e2.3.4 Network comparison\u003c/h2\u003e\u003cp\u003eWe conducted a \u003cem\u003eKruskal-Wallis\u0026rsquo;s\u003c/em\u003e test to analyze the average edge weights of the communities across the four networks. When significant differences were identified through the \u003cem\u003eKruskal-Wallis\u0026rsquo;s\u003c/em\u003e test, post-hoc pairwise comparisons were performed using \u003cem\u003eDunn's\u003c/em\u003e test to determine which specific community pairs exhibited significant differences in edge weights. To control for Type I errors, a Bonferroni correction was applied.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Demographic characteristics\u003c/h2\u003e\u003cp\u003eThe gender distribution among participants was approximately balanced, with ages ranging from 11 to 20 years (\u003cem\u003eMean\u003c/em\u003e\u0026thinsp;\u0026plusmn;\u0026thinsp;\u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;14.46\u0026thinsp;\u0026plusmn;\u0026thinsp;1.55). The majority of participants were of Han ethnicity, came from families with multiple children, were born in urban areas, and had parents with stable marital statuses. Additional demographic information is provided in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\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\u003eDemographic Information (N\u0026thinsp;=\u0026thinsp;1720)\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\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFrequency\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePercentage\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGender\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMale\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e882\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e51.28%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFemale\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e838\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e48.72%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJunior adolescence (Age 14 and under)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1054\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e61.28%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSenior adolescence (Age 15 and over)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e666\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e38.72%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEthnic\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHan\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1476\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e85.81%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMinor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e244\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e14.19%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFamily Fertility\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOnly-child families\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e406\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e23.60%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMulti-child families\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1314\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e76.40%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBirthplace\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUrban\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1578\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e91.74%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRural\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e142\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e8.26%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParents' marriage\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\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGood\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1594\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e92.67%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDivorced\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.33%\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=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Trajectories of loneliness symptoms\u003c/h2\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates four distinct trajectories of changes in loneliness symptoms: the stable low group, the increasing group, the decreasing group, and the stable high group. Out of 1,720 adolescents, 1,273 (74.01%) consistently scored below the critical threshold of 50 points on the UCLA Loneliness Scale (ULS), categorizing them into the stable low group. The increasing group, consisting of 60 adolescents (3.49%), had ULS scores below the critical threshold at T1 but exceeded the threshold at T2. The decreasing group, comprising 207 adolescents (12.03%), initially exhibited loneliness symptoms that gradually improved over time. Finally, adolescents who displayed positive loneliness symptoms at both time points were classified into the stable high group, which included 180 adolescents (10.47%).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Temporal networks across adolescence with distinct loneliness trajectories\u003c/h2\u003e\u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\u003ch2\u003e3.3.1 Network stability and accuracy\u003c/h2\u003e\u003cp\u003eThe accuracy plot reveals small to moderate confidence intervals surrounding the edge weights, suggesting that the CLPN model constructed from the four loneliness symptom trajectories demonstrates good accuracy (Supplementary Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). The results of case-drop bootstrapping indicate significant differences between the strongest and weakest edges (see Supplementary Fig. S2), thus affirming the accuracy of these edges (Epskamp \u0026amp; Fried, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Furthermore, the case-dropping results (see Supplementary Fig. S3) show that the four groups of out-EI, in-EI, and bridge-EI exhibit at least small to moderate stability. The network models derived from the four loneliness trajectories present the following centrality stabilities coefficients (CSs) for out-EI, in-EI, and bridge-EI: for the stable low group: bridge-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.75), in-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.52), out-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.60); for the increasing group: bridge-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.75), in-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.00), out-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.05); for the decreasing group: bridge-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.75), in-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.13), out-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.29); and for the stable high group: bridge-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.75), in-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.36), out-Expected Influence (CS\u0026thinsp;=\u0026thinsp;0.36). The centrality difference tests for edge weight variations are illustrated in Supplementary Figs. S4, S5, and S6.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec24\" class=\"Section3\"\u003e\u003ch2\u003e3.3.2 Network comparison\u003c/h2\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the findings from the Kruskal\u0026ndash;Wallis analyses and the subsequent Dunn post-hoc tests, which examine the mean edge weights within each community. Significant differences in edge weights\u0026mdash;both intra-community and inter-community\u0026mdash;were observed among all trajectory group pairs, with the exception of the Increasing\u0026ndash;Decreasing and Increasing\u0026ndash;Stable High group pairs.\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\u003eThe Kruskal-Walli\u0026rsquo;s test and Dunn test results of average edge weights between and within each community (N\u0026thinsp;=\u0026thinsp;1720).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\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\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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCommunity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eStable-low\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStable-High\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIncreasing\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eDecreasing\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eSignificant pairs\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLoneliness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnxiety\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIncreasing - Stable-high**\u003c/p\u003e\u003cp\u003eIncreasing - Stable-low **\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLoneliness \u0026rarr; IA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eDecreasing - Stable-high **\u003c/p\u003e\u003cp\u003eDecreasing - Stable-low***\u003c/p\u003e\u003cp\u003eIncreasing - Stable-low ***\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLoneliness \u0026rarr; Anxiety\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eDecreasing - Stable-low ***\u003c/p\u003e\u003cp\u003eIncreasing - Stable-low***\u003c/p\u003e\u003cp\u003eStable-high - Stable-low ***\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnxiety \u0026rarr; Loneliness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnxiety \u0026rarr; IA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIA \u0026rarr; Anxiety\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIncreasing - Stable-high **\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIA \u0026rarr; Loneliness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cb\u003eNote.\u003c/b\u003e *p\u0026thinsp;\u0026lt;\u0026thinsp;0.05, **p\u0026thinsp;\u0026lt;\u0026thinsp;0.01, ***p\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec25\" class=\"Section3\"\u003e\u003ch2\u003e3.3.3 Cross-Lagged panel network models\u003c/h2\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the cross-lagged panel network (CLPN) models corresponding to the four identified trajectories of loneliness symptoms. The detailed adjacency matrices for these networks are presented in supplementary Tables S1 through S4. To enhance the visual interpretability of the cross-lagged associations, autoregressive edges have been omitted from the primary network figures. Supplementary Fig. S7 offers an alternative network representation that includes both autoregressive and weaker edges. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the network centrality metrics\u0026mdash;out-Expected Influence, in-Expected Influence, and bridge-Expected Influence\u0026mdash;while comprehensive results are available in Supplementary Table S5.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSubstantial differences in edge weights were observed both within and across communities in the four loneliness trajectory CLPN models. Within-community differences were noted in the context of Anxiety, while between-community differences were identified in the following relationships: IA \u0026rarr; Anxiety, Loneliness \u0026rarr; IA, and Loneliness \u0026rarr; Anxiety, as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Additionally, the most prominent within-community cross-lagged edges for the stable low, increasing, decreasing, and stable high groups were as follows: 'Anticipation' (I4) \u0026rarr; 'Excessive use' (I2) (OR\u0026thinsp;=\u0026thinsp;1.22), 'Trouble relaxing' (A4) \u0026rarr; 'Nervousness' (A1) (OR\u0026thinsp;=\u0026thinsp;0.38), 'Uncontrollable worrying' (A2) \u0026rarr; 'Worry too much' (A3) (OR\u0026thinsp;=\u0026thinsp;1.36), and 'Salience' (I1) \u0026rarr; 'Excessive use' (I2) (OR\u0026thinsp;=\u0026thinsp;1.50). The most significant between-community cross-lagged edges included: 'Uncontrollable worrying' (A2) \u0026rarr; 'Social Isolation' (L1) (OR\u0026thinsp;=\u0026thinsp;1.17), 'Neglect work' (I3) \u0026rarr; 'Feeling afraid' (A7) (OR\u0026thinsp;=\u0026thinsp;1.29), 'Anticipation' (I4) \u0026rarr; 'Uncontrollable worrying' (A2) (OR\u0026thinsp;=\u0026thinsp;0.82), and 'Restlessness' (A5) \u0026rarr; 'Excessive use' (I2) (OR\u0026thinsp;=\u0026thinsp;1.20).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec26\" class=\"Section3\"\u003e\u003ch2\u003e3.3.4 Network inference\u003c/h2\u003e\u003cp\u003eThe results of the network centrality metrics are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In the stable low group, 'Social Isolation' (L1) exhibited the highest out-Expected Influence (OEI\u0026thinsp;=\u0026thinsp;2.48). In the increasing group, 'Nervousness' (A1) showed the highest out-EI (OEI\u0026thinsp;=\u0026thinsp;1.60). In the decreasing group, 'Worry too much' (A3) had the highest out-EI (OEI\u0026thinsp;=\u0026thinsp;2.34). Finally, in the stable high group, 'Excessive use' (I2) demonstrated the highest out-EI (OEI\u0026thinsp;=\u0026thinsp;2.70), indicating its strong predictive power over other symptoms within the network structure. In the stable low group, 'Uncontrollable worrying' (A2) exhibited the highest in-Expected Influence (IEI\u0026thinsp;=\u0026thinsp;1.63). In the increasing group, 'Restlessness' (A5) displayed the highest in-EI (IEI\u0026thinsp;=\u0026thinsp;1.37). In the decreasing group, 'Excessive use' (I2) had the highest in-EI (IEI\u0026thinsp;=\u0026thinsp;1.43). In the stable high group, 'Salience' (I1) had the highest in-EI (IEI\u0026thinsp;=\u0026thinsp;1.76), suggesting a strong vulnerability to the influence of other symptoms within the network. Furthermore, loneliness symptoms exhibited the highest bridge-Expected Influence (BEI) across all groups: in the stable low group (BEI\u0026thinsp;=\u0026thinsp;2.60 (L1), BEI\u0026thinsp;=\u0026thinsp;2.11 (L2)); in the increasing group (BEI\u0026thinsp;=\u0026thinsp;2.26 (L1), BEI\u0026thinsp;=\u0026thinsp;2.46 (L2)); in the decreasing group (BEI\u0026thinsp;=\u0026thinsp;2.38 (L1), BEI\u0026thinsp;=\u0026thinsp;2.28 (L2)); and in the stable high group (BEI\u0026thinsp;=\u0026thinsp;2.35 (L1), BEI\u0026thinsp;=\u0026thinsp;2.31 (L2)).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study conducts network modeling using longitudinal data from a large adolescent cohort, making it the first to demonstrate unique longitudinal correlations between loneliness, anxiety and IA across distinct trajectories of loneliness symptoms. Three main findings were identified: The structure of symptom networks related to loneliness, anxiety and IA differed across various trajectories of loneliness. Secondly, within the comorbidity networks, 'Social Isolation' (L1) in the stable low trajectory, 'Nervousness' (A1) in the increasing trajectory, 'Worry too much' (A3) in the decreasing trajectory, and 'Excessive use' (I2) in the stable high trajectory were identified as the most significant predictors of other symptoms. Third, 'Social Isolation' (L1) and 'Social Disconnectedness' (L2) were identified as the most prominent bridge symptoms in the comorbidity networks of all four loneliness trajectories.\u003c/p\u003e\u003cp\u003eTrajectory analysis identified four distinct developmental patterns of loneliness in Chinese adolescents: stable low (n\u0026thinsp;=\u0026thinsp;1273, 74.01%), increasing (n\u0026thinsp;=\u0026thinsp;60, 3.49%), decreasing (n\u0026thinsp;=\u0026thinsp;207, 12.03%), and stable high (n\u0026thinsp;=\u0026thinsp;180, 10.47%). The observed patterns correspond to the trajectory groupings identified in previous studies (Beattie et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chang et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hutten et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Qualter et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The distribution of participants among these trajectory groups did not fully align with prior findings. The increasing group constituted a larger proportion than previously reported, whereas both the decreasing and stable high groups were underrepresented compared to earlier studies (increasing: 37%; decreasing: 23%; stable high: 22%). The discrepancy between our findings and previous reports is most likely due to differences in assessment instruments, temporal measurement intervals, and cultural context (Olson et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The trajectory analysis shows that, despite the majority of teens appear to be free of significant loneliness, a significant portion continues to experience either increasing or stable high levels. This emphasizes the significance of constant surveillance and intervention efforts to combat loneliness and related disorders.\u003c/p\u003e\u003cp\u003eIn the directed network model of the stable-low group identifies 'Social Isolation' (L1) as a strong predictor of IA and anxiety symptoms. This finding is consistent with previous research, shown that social isolation is a key component in the onset and prediction of IA and anxiety symptoms, even in groups with relatively low levels of loneliness (Liang et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The comorbidity between loneliness and social anxiety is especially prominent in adolescents, with growing levels of loneliness aggravate social anxiety symptoms. The development of social anxiety can exacerbate feelings of loneliness, consequently perpetuating a negative feedback loop (Eres et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Loneliness has been recognized as a significant risk factor for IA within the realm of digital interaction (Saadati et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Likewise, neuroscience research aligns with our study. Research has identified an abnormal correlation between social isolation and the functioning of the Default Mode Network (DMN), perhaps leading individuals to experience discomfort in genuine social interactions, so driving them to find refuge in the virtual realm, consequently heightening the risk of IA (Cerniglia et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Reed et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Moreover, social isolation is intricately associated with the heightened activation of the hypothalamic-pituitary-adrenal (HPA) axis, leading to increased cortisol levels that intensify anxiety symptoms (Kubo et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Reed et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). According to the Model of Compensatory Use, people may turn to virtual sociability to cope with actual loneliness, while this emotional isolation can lead to online addiction (Cauberghe et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This proactive engagement with the internet may unconsciously increase anxiety levels, creating an undesirable cycle (Hern\u0026aacute;ndez et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn the Increasing group, the symptom of 'Nervousness' (A1) within the anxiety community demonstrates the highest OEI, indicating that anxiety symptoms may significantly predict the rise of loneliness among adolescents. According to research, an increase of anxiety symptoms significantly boosts feelings of loneliness, especially in adolescents with deteriorating social connections (Campagne, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Nguyen et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Furthermore, it is important to note that the interaction between anxiety and loneliness, as well as internet addiction behaviors, is bidirectional; loneliness and internet addiction can increase anxiety symptoms, leading to a vicious cycle (Hern\u0026aacute;ndez et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Cognitive Behavioral Therapy (CBT) aimed at addressing adolescent-specific anxiety symptoms, along with mindfulness-based therapies, may prove to be advantageous approaches for reducing the increasing severity of loneliness in adolescents (Goldin et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn the symptom network of the decreasing group of adolescent loneliness, the anxiety symptom 'Worry too much' (A3) had the most predictive influence on loneliness, IA, and anxiety symptoms. 'Worry too much', a core symptom of anxiety disorders (Fico et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e),, directly exacerbates anxiety symptoms and, through complex psychological mechanisms, contributes to the growth of loneliness and IA. According to O'Connor et al. (2023), adolescents with higher levels of loneliness are more likely to worry excessively about future uncertainty, which can worsen their anxiety symptoms (O\u0026rsquo;Connor et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Adolescents who worry excessively are more likely to seek emotional and social assistance online in order to cope with stress and uncertainty (Cauberghe et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Effective interventions addressing 'Worry too much' (A3) and related anxiety symptoms may reduce loneliness and hence improve teenagers' psychological well-being.\u003c/p\u003e\u003cp\u003eIn the symptom network structure of the stable-high loneliness group among adolescents, the symptom of 'Excessive use' (I2) associated with IA had the strongest predictive effect on loneliness, IA, and anxiety symptoms. This highlights that IA may significantly contribute to the constant feeling of loneliness. This study's findings reveal that the primary symptom of IA is 'Excessive use' (I2), which is consistent with previous research (Sha et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Over time, 'Excessive use' (I2) heightens the individual's demand for internet use, resulting in increased tolerance, which in turn sustains and worsens symptoms of internet addiction (Tiego et al., \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The continuous dependence of adolescents on the internet may mitigate feelings of loneliness and anxiety (Hern\u0026aacute;ndez et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, this type of escapism impairs their ability to face real-life issues, resulting in a vicious loop (Tadpatrikar et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)..\u003c/p\u003e\u003cp\u003eInterestingly, we found that in the four loneliness trajectory groups, the Indices of in-Expected Influence (IEIs) for the bridge symptoms 'Social Isolation' (L1) and 'Social Disconnectedness' (L2) were both less than one (Supplementary Fig. S2). This finding indicates that loneliness is negatively correlated with other symptoms. Loneliness symptoms may be alleviated or diminished under specific circumstances. Adolescents who experience loneliness may seek social support online and engage in self-soothing behaviors (Cauberghe et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, this positive aim may not be beneficial in the long term, and as proven by our study findings, it may exacerbate the chronic and complexities of loneliness. Our findings suggest that whether loneliness causes distress or exacerbates the complexity of mental disorder treatments and psychological issues, loneliness (particularly social isolation) as a transdiagnostic factor should be a key focus for preventive interventions aimed at IA and anxiety.\u003c/p\u003e"},{"header":"5. Limitation and future research","content":"\u003cp\u003eDespite its novel investigation of the relationship between IA, loneliness, and anxiety symptoms across distinct loneliness trajectories among adolescents, this study has certain limitations. First, the two-wave design limits the ability to notice subtle shifts in symptoms and prevents tracking their dynamic changes with exquisite temporal resolution. Future research may integrate ecological momentary assessment (EMA) with longitudinal methods, facilitating more accurate and regular monitoring of symptom variations and their interconnections. Second, the study was conducted solely with a non-clinical sample. While it provides basic information about the links between IA, loneliness, and anxiety symptoms in the general population, the diversity of mental diseases needs future expansion to clinical groups. Third, the study focused on Chinese adolescents; while the findings capture key elements of this population, their ecological validity is limited due to reliance on a single cultural background. Future research should expand its focus to encompass samples from varied cultural and cross-national populations to assess the generalizability and applicability of the results. Fourth, the trajectory groups demonstrated low centrality indices (out-EI, in-EI), warranting careful interpretation(Epskamp, S. et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In conclusion, the CLPN approach is restricted to proposing potential causal relationships; therefore, further experimental research is necessary to validate these findings.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis study presents the first evidence of significant difference in the network structure of symptoms linked to loneliness, anxiety and IA across different loneliness trajectories in teenagers, highlighting the diversity of loneliness and its accompanying mental issues. Furthermore, the data show that 'Social Isolation' (L1), 'Nervousness' (A1), 'Worry too much' (A3), and 'Excessive usage' (I2) are key symptoms in the different trajectories of loneliness development. Finally, our findings show that loneliness symptoms act as a connection in the comorbid network of IA and anxiety, connecting multiple mental health issues. The findings of this study establish theoretical basis for the development of more comprehensive effective intervention strategies targeted at enhancing adolescent mental health and overall well-being.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eYuntai Wang conceived the study, designed the study, performed the statistical analysis, interpreted the data, coordinated, and drafted the manuscript; Zijuan Ma helped to design the study and drafted the manuscript; Shiyi Lin interpreted the data, performed the statistical analysis, and conducted the measurements; Guodong Gong interpreted the data, performed the statistical analysis, and conducted the measurements; and Xiaoyi Huang interpreted the data and performed the measurements. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eNone.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAwn MA, Mohroofi AD, Alsaqer JK, Aljowder AA, Mohroofi AD, Alsuliti MA (2023) Impact of covid-19 outbreak on the behavior of children and adolescents in the Kingdom of Bahrain. Medicine 102(45):e35925. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1097/md.0000000000035925\u003c/span\u003e\u003cspan address=\"10.1097/md.0000000000035925\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBarreto M, Victor C, Hammond C, Eccles A, Richins MT, Qualter P (2021) Loneliness around the world: Age, gender, and cultural differences in loneliness. 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PLoS ONE 18(7):e0283862. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0283862\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0283862\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Adolescence, Loneliness, Internet Addiction, Anxiety, Network analysis, Cross-lagged panel network design","lastPublishedDoi":"10.21203/rs.3.rs-7920077/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7920077/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003ePurpose\u003c/h2\u003e\u003cp\u003eLoneliness is a prevalent psychological issue among adolescents. Anxiety and internet addiction (IA) are the most closely associated negative consequences of loneliness. Although prior research found a significant connection between the three, many of them overlooked individuals' distinct loneliness trajectories and their directional relationship at the symptom level. The purpose of this study was to identify complicated relationships and comorbidity models linking loneliness, anxiety, and IA across distinct trajectories of loneliness among adolescents.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eThe sample consisted of 1,720 adolescents from Yunnan, China, with data collected at two time points: T1 (October 2024) and T2 (March 2025). The UCLA Loneliness Scale (ULS), the Generalized Anxiety Disorder 7-item scale (GAD-7), and the Internet Addiction Test (IAT) were used to conduct the assessments. Cross-lagged panel network models were employed to investigate the various longitudinal associations between loneliness, anxiety, and IA symptoms over loneliness trajectories.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eFour distinct loneliness trajectories were identified: stable low, growing, decreasing, and stable high. The stable low trajectory was defined by 'Social isolation' (L1), the increasing trajectory by 'Nervousness' (A1), the decreasing trajectory by 'Worry too much' (A3), and the stable high trajectory by 'Excessive use' (I2). Loneliness sensations acted as bridge symptoms, connecting various elements of the network.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e\u003cp\u003eThis innovative study demonstrates distinct loneliness trajectories and their bridging role in the comorbid network, providing vital insights for personalized mental health therapies to reduce loneliness, anxiety and IA.\u003c/p\u003e","manuscriptTitle":"Dynamic Interplay Between Internet Addiction and Anxiety Across Distinct Loneliness Trajectories in Adolescents: A Cross-Lagged Panel Network Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-31 04:42:04","doi":"10.21203/rs.3.rs-7920077/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d32d7d58-fee8-4001-85a5-a0a89099fd74","owner":[],"postedDate":"October 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-21T17:23:22+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-31 04:42:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7920077","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7920077","identity":"rs-7920077","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}