{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T01:41:56Z","timestamp":1779154916000,"version":"3.51.4"},"reference-count":7,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5337,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper considers a probabilistic graph in which the points are perfectly reliable but the edges operate independently of one another, all with some known probability <jats:italic>p<\/jats:italic>. The graph <jats:italic>G<\/jats:italic> is in an operating state if the surviving edges induce a spanning connected subgraph of <jats:italic>G<\/jats:italic>. The all\u2010terminal reliability <jats:italic>R(G,p)<\/jats:italic> of <jats:italic>G<\/jats:italic> is the probability that <jats:italic>G<\/jats:italic> is in an operating state. A graph transformation, called \u201cthe swing surgery,\u201d is introduced, and it is shown that this surgery has important properties. First, if <jats:italic>H<\/jats:italic> is the graph obtained by deleting <jats:italic>m<\/jats:italic> independent edges from the complete graph, then for any other graph <jats:italic>G<\/jats:italic> with the same number of points and edges as <jats:italic>H, R(H,p)<\/jats:italic> &gt; <jats:italic>R(G,p)<\/jats:italic> for all 0 &lt; <jats:italic>p<\/jats:italic> &lt; 1. Moreover, the swing surgery yields a simple topological proof of the well\u2010known result that <jats:italic>H<\/jats:italic> has more spanning trees than does <jats:italic>G<\/jats:italic>. Another important consequence is that given any graph <jats:italic>G<\/jats:italic> there exists a threshold graph <jats:italic>T<\/jats:italic> with the same number of points and edges as <jats:italic>G<\/jats:italic> such that <jats:italic>R(T,p)<\/jats:italic> \u2264 <jats:italic>R(G,p)<\/jats:italic> for all 0 &lt; <jats:italic>p<\/jats:italic> &lt; 1.<\/jats:p>","DOI":"10.1002\/net.3230220206","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T12:18:02Z","timestamp":1178972282000},"page":"209-216","source":"Crossref","is-referenced-by-count":33,"title":["A reliability\u2010improving graph transformation with applications to network reliability"],"prefix":"10.1002","volume":"22","author":[{"given":"A.","family":"Satyanarayana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Schoppmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C. L.","family":"Suffel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230210204"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/26.61483"},{"key":"e_1_2_1_4_2","volume-title":"Algorithmic Graph Theory and Perfect Graphs","author":"Golumbic M. C.","year":"1980"},{"key":"e_1_2_1_5_2","volume-title":"Graph Theory","author":"Harary F.","year":"1972"},{"key":"e_1_2_1_6_2","first-page":"627","article-title":"The analysis of redundancy networks","volume":"39","author":"Moskowitz F.","year":"1958","journal-title":"AIEE Trans. Commun. Electron."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230210404"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.078B.023"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230220206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230220206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T20:12:39Z","timestamp":1698091959000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230220206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["10.1002\/net.3230220206"],"URL":"https:\/\/doi.org\/10.1002\/net.3230220206","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}