Key node identification for a network topology using hierarchical comprehensive importance coefficients

Key node identification for a network topology using hierarchical comprehensive importance coefficients | 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 Key node identification for a network topology using hierarchical comprehensive importance coefficients Fanshuo Qiu, Chengpu Yu, Yunji Feng, Yao Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3964023/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Key nodes are similar to important hubs in a network structure, which can directly determine the robustness and stability of the network. By effectively identifying and protecting these critical nodes, the robustness of the network can be improved, making it more resistant to external interference and attacks. There are various topology analysis methods for existing networks, but key node identification methods often only focus on local attributes or global attributes. Designing an algorithm that combines both attributes can improve the accuracy of key node identification. In this paper, the constraint coefficient of a weakly connected network is calculated based on the Salton indicator, and the hierarchical tenacity global coefficient is obtained by an improved K-Shell decomposition method. Then, a hierarchical comprehensive node importance identification algorithm is proposed which can comprehensively indicate the local and global attributes of the network nodes. Experimental results on real network datasets show that the proposed algorithm outperforms the other classic algorithms in terms of connectivity, average remaining edges, sensitivity and monotonicity. Physical sciences/Mathematics and computing Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 12 Apr, 2024 Reviews received at journal 08 Apr, 2024 Reviews received at journal 03 Apr, 2024 Reviewers agreed at journal 25 Mar, 2024 Reviewers agreed at journal 20 Mar, 2024 Reviewers invited by journal 19 Mar, 2024 Editor assigned by journal 19 Mar, 2024 Editor invited by journal 11 Mar, 2024 Submission checks completed at journal 10 Mar, 2024 First submitted to journal 17 Feb, 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. 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-3964023","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":278075438,"identity":"0ab935f5-51a6-48f2-b6de-ec1f200f2951","order_by":0,"name":"Fanshuo Qiu","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Fanshuo","middleName":"","lastName":"Qiu","suffix":""},{"id":278075439,"identity":"2f88862c-016d-4ccf-a7b8-e8fd83ffe49a","order_by":1,"name":"Chengpu Yu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYHACNgjF3sNwAEgxNhCvhecMw4EDpGmRyGFgIEqLwY3kZw8+7qjNM7j59uDhDww2shsOMD97gF9LmrnhzDPHiw1u5yUAHZZmvOEAm7kBfi05bNK8bccSN9zOMQBqOZy44QAPmwRBLX9BWm6eAWn5T6QWxraaxA03eEBaDhDWInnmmZlkb9uBYskzQL+cMUg2nnmYzQyvFr7jyc8kfrbV5fEdP3v4Q0WFnWzf8eZneLUoHABThxOg7gRiZnzqgUC+AUzVJRBQNwpGwSgYBSMZAAB65VZTSssAhwAAAABJRU5ErkJggg==","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Chengpu","middleName":"","lastName":"Yu","suffix":""},{"id":278075440,"identity":"24c169fb-7942-44bd-a7b3-f0878c26a434","order_by":2,"name":"Yunji Feng","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yunji","middleName":"","lastName":"Feng","suffix":""},{"id":278075441,"identity":"512c9a2a-0397-481d-9954-1d7833beb7f1","order_by":3,"name":"Yao Li","email":"","orcid":"","institution":"Beijing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yao","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-02-17 12:16:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3964023/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3964023/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52580751,"identity":"b25d9c00-25fc-4380-980b-adda70fdc677","added_by":"auto","created_at":"2024-03-13 08:13:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":845275,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3964023/v1_covered_dd97b123-0b66-43a8-813f-85e5f2629a90.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Key node identification for a network topology using hierarchical comprehensive importance coefficients","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3964023/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3964023/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eKey nodes are similar to important hubs in a network structure, which can directly determine the robustness and stability of the network. By effectively identifying and protecting these critical nodes, the robustness of the network can be improved, making it more resistant to external interference and attacks. There are various topology analysis methods for existing networks, but key node identification methods often only focus on local attributes or global attributes. Designing an algorithm that combines both attributes can improve the accuracy of key node identification. In this paper, the constraint coefficient of a weakly connected network is calculated based on the Salton indicator, and the hierarchical tenacity global coefficient is obtained by an improved K-Shell decomposition method. Then, a hierarchical comprehensive node importance identification algorithm is proposed which can comprehensively indicate the local and global attributes of the network nodes. Experimental results on real network datasets show that the proposed algorithm outperforms the other classic algorithms in terms of connectivity, average remaining edges, sensitivity and monotonicity.\u003c/p\u003e","manuscriptTitle":"Key node identification for a network topology using hierarchical comprehensive importance coefficients","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-13 08:05:03","doi":"10.21203/rs.3.rs-3964023/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-04-12T04:52:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-08T08:53:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-03T09:29:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8fb9c869-6f61-4dbf-b1e8-8b040af8693d","date":"2024-03-25T08:02:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"282d7648-f877-432d-b8d8-74ebf432c87e","date":"2024-03-20T09:41:01+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-19T17:34:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-03-19T17:21:55+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-11T04:32:21+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-10T12:49:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-02-17T12:05:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ae2a7545-be39-47ef-82b9-4b9615e252fd","owner":[],"postedDate":"March 13th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":29289203,"name":"Physical sciences/Mathematics and computing"},{"id":29289204,"name":"Physical sciences/Mathematics and computing/Applied mathematics"}],"tags":[],"updatedAt":"2024-05-22T07:15:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-13 08:05:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3964023","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3964023","identity":"rs-3964023","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}