{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T11:58:20Z","timestamp":1768996700557,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Kunlun Talent","award":["2023-QLGKLYCZX-027"],"award-info":[{"award-number":["2023-QLGKLYCZX-027"]}]},{"name":"Kunlun Talent","award":["2023021wys019"],"award-info":[{"award-number":["2023021wys019"]}]},{"name":"A Study of Reliability Indicators for Complex Networks and Their Applications","award":["2023-QLGKLYCZX-027"],"award-info":[{"award-number":["2023-QLGKLYCZX-027"]}]},{"name":"A Study of Reliability Indicators for Complex Networks and Their Applications","award":["2023021wys019"],"award-info":[{"award-number":["2023021wys019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability.<\/jats:p>","DOI":"10.3390\/axioms13070459","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T09:01:19Z","timestamp":1720429279000},"page":"459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Method for Calculating the Reliability of 2-Separable Networks and Its Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Jing","family":"Liang","sequence":"first","affiliation":[{"name":"School of Computer and Information Science, Qinghai Institute of Technology, Xining 810016, China"},{"name":"School of Computer Technology and Applications, Qinghai University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haixing","family":"Zhao","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, China"},{"name":"Academy of Plateau, Science and Sustainability, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sun","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qinghai University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/(SICI)1097-0037(200003)35:2<109::AID-NET2>3.0.CO;2-N","article-title":"Network reliability with node failures","volume":"35","author":"Liu","year":"2000","journal-title":"Networks"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.dam.2019.04.022","article-title":"Classes of uniformly most reliable graphs for all-terminal reliability","volume":"267","author":"Archer","year":"2019","journal-title":"Discret. 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