Willingness Centrality: A New Centrality Measure Based on the Number of Edges Participating in Cycles

Willingness Centrality: A New Centrality Measure Based on the Number of Edges Participating in Cycles | 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 Willingness Centrality: A New Centrality Measure Based on the Number of Edges Participating in Cycles Mahdi Esmailnia Kivi, Saeid Taghavi Afshord, Asgarali Bouyer, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4440440/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 Researchers of complex networks have always sought to discover hidden information in networks. Centrality measures are quantitative data used to display information that cannot be seen at first glance in the network and indicate the importance of a node or edge. Due to the limitation of processing power and the complexity of real-world problems, processes are moving towards localization. This paper proposes a new method to represent edge importance based on the number of edges involved in 3 and 4-cycles. Also, an algorithm with O(n*((m/n)^2)) time complexity is presented to find these cycles. The number assigned to each edge indicates how many times it appears in short cycles. The delta coefficient is defined to increase the effect of 3-cycles. This measure can be calculated for nodes by summing the centrality of edges and dividing by two. Using the willingness centrality measure in issues such as community detection and its acceptable result shows the practicality of the proposed method. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4440440","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":310153654,"identity":"fdcd9687-1b11-466f-a1a6-d9bdd95743c4","order_by":0,"name":"Mahdi Esmailnia Kivi","email":"","orcid":"","institution":"Islamic Azad University Shabestar","correspondingAuthor":false,"prefix":"","firstName":"Mahdi","middleName":"Esmailnia","lastName":"Kivi","suffix":""},{"id":310153655,"identity":"13680c38-82bc-4d7c-9b5e-81b3d22ac420","order_by":1,"name":"Saeid Taghavi Afshord","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIie2RMQrCQBBFZ1jQZoNtCiVXWHuDV0nIHawTFjaNmjbiJXKElSlsxNrCIiJYWZhORUGDYJnVTnBf9+E/5sMAWCy/iwZgTOtXwNhUrxu10gq+VYCLzxZ5qW6X5+vWE0te6YsCrxMzdWpSxCrAZDI99AtyisVEQT/XKPNGBQKMnTHhTDqFdhRgASibh2UlJvcxDWeSl4u7gqFRgU2Akp8pzBgHel4JjYrY7JJ5L6YoYy1B3bUb5WQcFunqeCNfdWhfHUcDP0vTffOw+i2o3sl9/tQgvLh91LJYLJZ/5QEADk76FiD0KgAAAABJRU5ErkJggg==","orcid":"","institution":"Islamic Azad University Shabestar","correspondingAuthor":true,"prefix":"","firstName":"Saeid","middleName":"Taghavi","lastName":"Afshord","suffix":""},{"id":310153657,"identity":"c9483799-e421-4923-8837-11a76488a1de","order_by":2,"name":"Asgarali Bouyer","email":"","orcid":"","institution":"Azarbaijan Shahid Madani University","correspondingAuthor":false,"prefix":"","firstName":"Asgarali","middleName":"","lastName":"Bouyer","suffix":""},{"id":310153658,"identity":"e46e3990-0669-45eb-94b7-c04b13edf094","order_by":3,"name":"Vahid Majidnezhad","email":"","orcid":"","institution":"Islamic Azad University Shabestar","correspondingAuthor":false,"prefix":"","firstName":"Vahid","middleName":"","lastName":"Majidnezhad","suffix":""}],"badges":[],"createdAt":"2024-05-18 09:37:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4440440/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4440440/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58240782,"identity":"130f4a1c-623f-4932-95be-88508144bf03","added_by":"auto","created_at":"2024-06-13 01:16:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":849877,"visible":true,"origin":"","legend":"","description":"","filename":"wlc.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4440440/v1_covered_5afe4a89-9444-4e7b-a800-b935ad3c5848.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Willingness Centrality: A New Centrality Measure Based on the Number of Edges Participating in Cycles","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-4440440/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4440440/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eResearchers of complex networks have always sought to discover hidden information in networks. Centrality measures are quantitative data used to display information that cannot be seen at first glance in the network and indicate the importance of a node or edge. Due to the limitation of processing power and the complexity of real-world problems, processes are moving towards localization. This paper proposes a new method to represent edge importance based on the number of edges involved in 3 and 4-cycles. Also, an algorithm with O(n*((m/n)^2)) time complexity is presented to find these cycles. The number assigned to each edge indicates how many times it appears in short cycles. The delta coefficient is defined to increase the effect of 3-cycles. This measure can be calculated for nodes by summing the centrality of edges and dividing by two. Using the willingness centrality measure in issues such as community detection and its acceptable result shows the practicality of the proposed method.\u003c/p\u003e","manuscriptTitle":"Willingness Centrality: A New Centrality Measure Based on the Number of Edges Participating in Cycles","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-04 06:55:56","doi":"10.21203/rs.3.rs-4440440/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":"65df7c36-f74f-4029-a639-6ea8dc21a4b0","owner":[],"postedDate":"June 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-13T01:08:30+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-04 06:55:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4440440","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4440440","identity":"rs-4440440","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}