Graphlet-Based Edge Weighting for Improved Community Detection in Complex Networks

Graphlet-Based Edge Weighting for Improved Community Detection in Complex 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 Research Article Graphlet-Based Edge Weighting for Improved Community Detection in Complex Networks Anstasiia Dziuba, Jure Pražnikar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9182150/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 14 You are reading this latest preprint version Abstract Community detection is essential for uncovering the functional organization of complex networks. While traditional methods often rely on edge density, motif-based approaches use higher-order structural patterns to identify communities. However, existing research frequently employs conventional motifs, such as triangles or 4-node cliques, or lacks validation against networks with ground-truth communities. This study addresses these limitations by systematically evaluating eight small motifs across both synthetic and real-world networks with known community structures. We propose a framework that transforms unweighted graphs into weighted representations by assigning weights to node pairs based on their co-occurrence frequency within specific graphlets, while also preserving information about the original edges, rather than creating a potentially sparse (hyper)network. Thus, graphlet adjacency captures the topological complexity of a node by accounting for both its direct edges and the local connectivity patterns of its neighbors; this higher-order information is vital for accurate community detection. Our results demonstrate that graphlet-based weighting significantly enhances community detection in networks. We find that no single "universal" motif optimizes performance across all real-world networks. Contrary to the prevailing emphasis on dense, clique-based structures, our findings reveal that simple path-like motifs often yield superior performance in real-world networks. These results suggest that relying exclusively on cliques may overlook critical connectivity patterns, offering a new perspective on how higher-order structures define communities in networks. community network graphlets small-motif Full Text Additional Declarations No competing interests reported. Supplementary Files Supplement.pdf Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 05 May, 2026 Reviews received at journal 01 May, 2026 Reviews received at journal 26 Apr, 2026 Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 06 Apr, 2026 Reviews received at journal 05 Apr, 2026 Reviewers agreed at journal 05 Apr, 2026 Reviewers agreed at journal 04 Apr, 2026 Reviewers agreed at journal 04 Apr, 2026 Reviewers agreed at journal 04 Apr, 2026 Reviewers invited by journal 04 Apr, 2026 Editor assigned by journal 01 Apr, 2026 Submission checks completed at journal 01 Apr, 2026 First submitted to journal 20 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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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-9182150","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":618522475,"identity":"430b1981-6751-4496-a9a8-f15c1c786603","order_by":0,"name":"Anstasiia Dziuba","email":"","orcid":"","institution":"University of Primorska","correspondingAuthor":false,"prefix":"","firstName":"Anstasiia","middleName":"","lastName":"Dziuba","suffix":""},{"id":618522476,"identity":"6dd9abd4-721a-4e26-8463-ea7e30e82139","order_by":1,"name":"Jure Pražnikar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYBACxgYEsxlI2EDYCSRoSSOsBRkwA/FhIpTNyH34gHHHPXn52c3NBj/3nE/cLn2A+cMDfA6bkW5swHim2LBxzsHmxJ5ntxN39iWwSeBzGOOMNDYJxrYExmaJxOYDPAduJ244w8CG3/sz0th/ALXYtwG1HPxz4BxIC/MHQrYwALUk9gC1JPMcOADSwoDfYT3PmCUSzyQkzwBqMZY5kGy8s4exDa8Ww/Y0xg8fdyTYzp+R/ljyzQE72e08zIc//sCnpQFIJDYgiRggRy82IA92HaqWUTAKRsEoGAWoAABqCU8zh0JdLAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Primorska","correspondingAuthor":true,"prefix":"","firstName":"Jure","middleName":"","lastName":"Pražnikar","suffix":""}],"badges":[],"createdAt":"2026-03-20 22:23:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9182150/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9182150/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106959733,"identity":"6f1e8788-9f70-4ce7-96a7-2f2bac3ff56d","added_by":"auto","created_at":"2026-04-15 09:14:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6358443,"visible":true,"origin":"","legend":"","description":"","filename":"GraphletsCommunitySpringer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9182150/v1_covered_b9204e68-8114-42a0-8060-b31a57be73e6.pdf"},{"id":106745417,"identity":"fecd8dff-e06c-4083-b47e-d81bfc0c101d","added_by":"auto","created_at":"2026-04-13 05:26:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1371675,"visible":true,"origin":"","legend":"","description":"","filename":"Supplement.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9182150/v1/38a37ce8ef018f0379f7cb56.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Graphlet-Based Edge Weighting for Improved Community Detection in Complex Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-intelligent-information-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jiis","sideBox":"Learn more about [Journal of Intelligent Information Systems](http://link.springer.com/journal/10844)","snPcode":"10844","submissionUrl":"https://submission.nature.com/new-submission/10844/3","title":"Journal of Intelligent Information Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"community, network, graphlets, small-motif","lastPublishedDoi":"10.21203/rs.3.rs-9182150/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9182150/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Community detection is essential for uncovering the functional organization of complex networks. 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