EFB-GNN: Energy-Centric Spectral Fourier–Bayesian Control and Community Dynamics Detection in Graph Neural Network System

EFB-GNN: Energy-Centric Spectral Fourier–Bayesian Control and Community Dynamics Detection in Graph Neural Network System | 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 EFB-GNN: Energy-Centric Spectral Fourier–Bayesian Control and Community Dynamics Detection in Graph Neural Network System Yanfei Ma, Daozheng Qu, Yibo Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8867083/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 Community detection in attributed graphs is extremely sensitive to minor structural and feature perturbations, frequently resulting in sudden assignment alterations despite competitive clustering accuracy in pristine conditions. This illusory instability undermines the trustworthiness of graph learning models in real-world contexts where noise, dynamic evolution, and structural uncertainty are inevitable. In this study, we introduce EFB-GNN, an Energy-centric Fourier–Bayesian Graph Neural Network that explicitly incorporates spectral stability regulation, Bayesian uncertainty modeling, and community-aware message control into a cohesive framework. The model restricts the spectrum response of graph propagation operators by polynomial Fourier filtering, while variational Bayesian inference assesses epistemic uncertainty. Comprehensive experiments on various real-world graphs, ranging from weak to strong homophily, sparse to dense connectivity, and small to large scales, reveal that EFB-GNN consistently mitigates assignment drift amid both structural and feature perturbations while preserving competitive clustering accuracy. The sensitivity analysis within regulated spectral gap conditions verifies that the proposed framework attains significant stability improvements without causing representation collapse or undue smoothing. These findings confirm stability-aware community discovery as a systematic enhancement of graph representation learning, integrating spectral graph theory, probabilistic inference, and resilient graph modeling. Physical sciences/Mathematics and computing Physical sciences/Physics 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-8867083","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":593697463,"identity":"884efd55-2ff8-47f0-a5e4-a59fa6051e7b","order_by":0,"name":"Yanfei Ma","email":"","orcid":"","institution":"Fairleigh Dickinson University","correspondingAuthor":false,"prefix":"","firstName":"Yanfei","middleName":"","lastName":"Ma","suffix":""},{"id":593697464,"identity":"1142b2ce-c22c-4815-8521-c339bfaaf92d","order_by":1,"name":"Daozheng Qu","email":"","orcid":"","institution":"Fairleigh Dickinson University","correspondingAuthor":false,"prefix":"","firstName":"Daozheng","middleName":"","lastName":"Qu","suffix":""},{"id":593697465,"identity":"14deae67-c1a1-414d-a81b-79cae5ec447c","order_by":2,"name":"Yibo Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYNACgwMM/Mwka5FsJtGaAyBdxJp//Ozh1zwFd+SMjzMffPCBwSZf3oGQljN5adY8Bs+MzQ6zJRvOYEiz3EjIOrMDOWbGPAaHE7cd5jGT5mE4bGDYQEjL+TcQLZub+b///kOUlhs5xo9BWjYw87ABw/mwgTwBHQz2N96YMc4B+kXiMJuxZI9BmoEBIS2S/TnGH978uSPH33/44YcfFTYG8oQcBgRsUjxwtgEDURHE/PEHMpcYW0bBKBgFo2BkAQDpokDR+nWI2AAAAABJRU5ErkJggg==","orcid":"","institution":"University of California, San Diego","correspondingAuthor":true,"prefix":"","firstName":"Yibo","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2026-02-13 03:53:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8867083/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8867083/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105727477,"identity":"8da66dca-10f9-4a2c-a380-dd14240364bb","added_by":"auto","created_at":"2026-03-30 10:43:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6944110,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8867083/v1_covered_03f946f2-45be-43f6-8ae0-07115800efaf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eEFB-GNN: Energy-Centric Spectral Fourier–Bayesian Control and Community Dynamics Detection in Graph Neural Network System\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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-8867083/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8867083/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Community detection in attributed graphs is extremely sensitive to minor structural and feature perturbations, frequently resulting in sudden assignment alterations despite competitive clustering accuracy in pristine conditions. 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