Learning about the liveability of cities from young migrants using the combinatorial-Hodge-theory approach

Learning about the liveability of cities from young migrants using the combinatorial-Hodge-theory approach | 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 Article Learning about the liveability of cities from young migrants using the combinatorial-Hodge-theory approach Takaaki Aoki, Kohei Nagamachi, Tetsuya Shimane This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5575866/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Oct, 2025 Read the published version in npj Urban Sustainability → Version 1 posted 12 You are reading this latest preprint version Abstract Migration is a major decision to leave one place and move to another, involving career and life changes. Migration flows provide people's comparisons across places about which is better to live by ''vote with their feet'' (Tiebout, 1956). However, is it possible to derive a consistent measure of the liveability of cities from these flows? We propose a combinatorial-Hodge-theory approach: the empirical liveability of cities is evaluated by a potential governing unbalanced, acyclic migrations between cities. As a case study, we measure the liveability of municipalities in Japan for specific populations such as families with small children and women of reproductive age in a population-decline society. Using these potentials as dependent variables, we perform a regression analysis to identify the factors relevant to liveability. We also derive analytical expressions that allow us to interpret as potentials the standards of living or utilities, estimated in the economics literature (Douglas & Wall, 1993; Douglas, 1997; Douglas & Wall, 2000; Wall, 2001; Nakajima & Tabuchi, 2011). The proposed method extracts a consistent metric of interval scale from the non-transitive, pairwise comparison between locations and provides substantial statistics for urban planning by policymakers. Social science/Complex networks Social science/Environmental studies Hodge decomposition internal migration liveable cities mobility municipalities at risk of disappearing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Oct, 2025 Read the published version in npj Urban Sustainability → Version 1 posted Editorial decision: Revision requested 21 Mar, 2025 Reviews received at journal 11 Mar, 2025 Reviews received at journal 09 Mar, 2025 Reviews received at journal 07 Mar, 2025 Reviewers agreed at journal 19 Feb, 2025 Reviewers agreed at journal 19 Feb, 2025 Reviewers agreed at journal 19 Feb, 2025 Reviewers agreed at journal 08 Feb, 2025 Reviewers invited by journal 06 Jan, 2025 Editor assigned by journal 20 Dec, 2024 Submission checks completed at journal 17 Dec, 2024 First submitted to journal 03 Dec, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5575866","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":391385001,"identity":"039692e9-1435-4768-9d28-2f53bc565ef9","order_by":0,"name":"Takaaki Aoki","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIiWNgGAWjYFACNiA+IAFmHADxJdgbgKSBBU4NPJhaeECUgQQhLTDrQFokEsAUTi327McSP/w4Y8HA396WeICxzSZfcubzqxt+FEgARboTsNrCk3ZYsueGBIPEmWMHgFrSLGdL55Td7DEAiZzdgN1h6Q0SPB+AzriR3nCAcdthAznpnLQbPEAtBhK52LXwP2/++QeoRR6uRfJM2s0/+LRIpB2T5gE6zOBG2gGwFmkJ9mO38dpy41matcwZCR7DM8cSDiT+SzOQ7Mlhuy1jIMGDyy/s/WnGN98cq5OTO95m/OHDGRsDiePHn91888dGjr+9F6sWRDCAQAKEbYAQIRKwPyBF9SgYBaNgFAx/AACTtWMaD5rrKwAAAABJRU5ErkJggg==","orcid":"","institution":"Shiga University","correspondingAuthor":true,"prefix":"","firstName":"Takaaki","middleName":"","lastName":"Aoki","suffix":""},{"id":391385002,"identity":"cb9b3ff6-c569-4610-8143-46bdc1f7022c","order_by":1,"name":"Kohei Nagamachi","email":"","orcid":"","institution":"Kagawa University","correspondingAuthor":false,"prefix":"","firstName":"Kohei","middleName":"","lastName":"Nagamachi","suffix":""},{"id":391385003,"identity":"c8b40d44-4d5e-42b1-ad8a-c59b1705ca04","order_by":2,"name":"Tetsuya Shimane","email":"","orcid":"","institution":"Kagawa University","correspondingAuthor":false,"prefix":"","firstName":"Tetsuya","middleName":"","lastName":"Shimane","suffix":""}],"badges":[],"createdAt":"2024-12-04 02:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5575866/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5575866/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s42949-025-00270-4","type":"published","date":"2025-10-22T16:16:14+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94505745,"identity":"6f501ea1-015a-4b0e-9694-7d41d001b6a3","added_by":"auto","created_at":"2025-10-28 16:22:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":13692130,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5575866/v1_covered_6d15b742-77d0-410b-a758-c983d491fd9d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Learning about the liveability of cities from young migrants using the combinatorial-Hodge-theory approach","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-urban-sustainability","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjurbansustain","sideBox":"Learn more about [npj Urban Sustainability](https://www.nature.com/npjurbansustain/)","snPcode":"42949","submissionUrl":"https://submission.springernature.com/new-submission/42949/3","title":"npj Urban Sustainability","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Hodge decomposition, internal migration, liveable cities, mobility, municipalities at risk of disappearing","lastPublishedDoi":"10.21203/rs.3.rs-5575866/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5575866/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Migration is a major decision to leave one place and move to another, involving career and life changes. 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