Investigating the applicability of the survivability function for the Social Systems Analysis

Investigating the applicability of the survivability function for the Social Systems Analysis | 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 Investigating the applicability of the survivability function for the Social Systems Analysis Tatsuo Oyama, Kazuhiro Kobayashi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7508533/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 This paper investigates the applicability of the survivability function (SF), which was derived from the path counting problem we proposed for solving various types of complex problems occurring in our social systems. First, we define the connectivity function for a given network, and obtain the expected edge-deletion connectivity function (EEDCF) when an arbitrary number of edges are deleted from the original network. Asking the relationship between two ratios, i.e., the ratio of the number of edges deleted from the network to the total number of edges in the original network, and the ratio of the number of paths connecting two different vertices in the edge-deleted network to the total number of paths in the original network. Applying the Monte Carlo method, we estimate an approximating EEDCF by using a nonlinear function with two parameters, which we call the SF. The SF can be applied to solve various social problems such as measuring the robustness of the network-structured system, investigating Baran’s communication network, and approximating the relationship between vote share and seat share for the single-member voting system. Finally, we show the relationship among the cubic law, logistic function, and the SF. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Survivability function path counting problem connectivity function Monte Carlo method robustness of the network-structured system Baran’s communication network single-member voting system vote share seat share cubic law logistic function 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. 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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-7508533","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":527263846,"identity":"e9efa3ad-24ca-47a9-9ada-abe1cf5c6bf9","order_by":0,"name":"Tatsuo 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