Generalization of Hierarchical Clustering for Hidden Community Spillover Detection in Multilayer Networks

Generalization of Hierarchical Clustering for Hidden Community Spillover Detection in Multilayer Networks | 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 Generalization of Hierarchical Clustering for Hidden Community Spillover Detection in Multilayer Networks Jamshid Ardalankia, Ali Habibnia, Marcel Ausloos, Reza Jafari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4815070/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 Interdependent networks structurally influence each other so that the source network imposes hidden community structures into the target network. We propose a mathematical model that by generalizing hierarchical clustering for multilayer networks, finds some interlayer transmitted hidden community structures that are not detectable by conventional community detection methods. The proposed methodology reveals evidence for hidden interlayer interactions that consequently generate hidden links on the target network. These hidden links construct hidden community structures on the target network (imposed from the source network) that are distinct from the community structures of the solo target network (without the presence of the source network). This model applies to systems with hidden interlayer interactions such as covert criminal groups, inter-platform social network interactions, and financial markets. Criminal and terrorist groups use the "source layer" (e.g., video game networks) to manage, guide, and lead their criminal activities on the "target layer." These groups keep the interlayer interactions covert. The members form their communities on an online source layer and perform their activities on the target layer without leaving a footprint. Social networks on different platforms (layers) possess communities that influence each other. Financial markets are well known for complicated endogenous and exogenous, but often hidden, not to say the least, asymmetric layer interactions. In this research, we generalize hierarchical clustering to represent the hidden communities resulting from the spillover from one network to another. We implement our model on multilayer financial networks: in particular, we find that trading value logarithmic changes (source) impose hidden community structures on the price return network (target). The main finding is that adding another relevant layer such as the trading value layer adds more information to systemic behaviors throughout the price return network. Dismissing it may yield less systemic information and underestimation of systemic risk because the footprint of some structures on the target network is originated from another layer and is not detectable from singling out the target layer. Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-4815070","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":338121286,"identity":"ab3a7ec8-b2a4-4ba3-bdc8-83d089cbbbeb","order_by":0,"name":"Jamshid Ardalankia","email":"","orcid":"","institution":"Virginia Tech","correspondingAuthor":false,"prefix":"","firstName":"Jamshid","middleName":"","lastName":"Ardalankia","suffix":""},{"id":338121287,"identity":"9a0a5a73-c5c0-4542-a92c-6f02d43a28de","order_by":1,"name":"Ali Habibnia","email":"","orcid":"","institution":"Virginia Tech","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"","lastName":"Habibnia","suffix":""},{"id":338121288,"identity":"ac7e2866-c260-4cf0-aa88-a9cf6cf5597a","order_by":2,"name":"Marcel Ausloos","email":"","orcid":"","institution":"University of Leicester","correspondingAuthor":false,"prefix":"","firstName":"Marcel","middleName":"","lastName":"Ausloos","suffix":""},{"id":338121289,"identity":"63ab5a24-2c7b-4381-8645-02bbfe9981d0","order_by":3,"name":"Reza Jafari","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYFCCAwwfGBgk5MDMB0RqYZwB1GIMZiYQaQ1IC0NiA4hJlBZ5x8MPG37usUifH3b4IdAWOzndBgJaDA8cM2zseSaRu/F2mgFQS7Kx2QFCWhoOmD/gOQDUMjsBpOVA4jbCWo5/bPxzQCLdcHb6B+K0yDOcMWwG2pIgL51DpC0GDGcKm2UOSBhukM4pOJBgQIRf5Gcc39j45kCdvPzs9M0fPlTYyRHUYnADqsLgAMRSwkC+vwHKaCBC9SgYBaNgFIxMAACJMk2MeOowjgAAAABJRU5ErkJggg==","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":true,"prefix":"","firstName":"Reza","middleName":"","lastName":"Jafari","suffix":""}],"badges":[],"createdAt":"2024-07-28 04:08:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4815070/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4815070/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63002618,"identity":"2879f662-3692-41b4-b9dd-dee417f904ef","added_by":"auto","created_at":"2024-08-22 03:33:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":814012,"visible":true,"origin":"","legend":"","description":"","filename":"InterlayerStructuralSpilloverFINAL.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4815070/v1_covered_60cdee63-2195-4a45-a98e-2ea0ebe5d19e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Generalization of Hierarchical Clustering for Hidden Community Spillover Detection in Multilayer Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-4815070/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4815070/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Interdependent networks structurally influence each other so that the source network imposes hidden community structures into the target network. We propose a mathematical model that by generalizing hierarchical clustering for multilayer networks, finds some interlayer transmitted hidden community structures that are not detectable by conventional community detection methods. The proposed methodology reveals evidence for hidden interlayer interactions that consequently generate hidden links on the target network. These hidden links construct hidden community structures on the target network (imposed from the source network) that are distinct from the community structures of the solo target network (without the presence of the source network). This model applies to systems with hidden interlayer interactions such as covert criminal groups, inter-platform social network interactions, and financial markets. Criminal and terrorist groups use the \"source layer\" (e.g., video game networks) to manage, guide, and lead their criminal activities on the \"target layer.\" These groups keep the interlayer interactions covert. The members form their communities on an online source layer and perform their activities on the target layer without leaving a footprint. Social networks on different platforms (layers) possess communities that influence each other. Financial markets are well known for complicated endogenous and exogenous, but often hidden, not to say the least, asymmetric layer interactions. In this research, we generalize hierarchical clustering to represent the hidden communities resulting from the spillover from one network to another. We implement our model on multilayer financial networks: in particular, we find that trading value logarithmic changes (source) impose hidden community structures on the price return network (target). The main finding is that adding another relevant layer such as the trading value layer adds more information to systemic behaviors throughout the price return network. 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