{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T09:21:09Z","timestamp":1760606469132},"reference-count":5,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":9080,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1981,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper is concerned with the problem of computing the probability that a root vertex can communicate with all other vertices in a probabilistic directed graph. One method is to apply the inclusion\u2010exclusion principle of probability theory to the event \u201cat least one rooted spanning tree of the graph is working.\u201d We prove combinatorial properties of graphs which allow us to derive a much condensed form of the inclusion\u2010exclusion expression. Each term corresponds to an acyclic spanning subgraph of the original graph, with coefficient equal to (\u22121)<jats:sup><jats:italic>b<\/jats:italic>\u2010<jats:italic>n<\/jats:italic>+1<\/jats:sup>, where <jats:italic>b<\/jats:italic> and <jats:italic>n<\/jats:italic> are the number of edges and vertices of the subgraph, respectively.<\/jats:p>","DOI":"10.1002\/net.3230110405","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T12:50:51Z","timestamp":1178887851000},"page":"357-366","source":"Crossref","is-referenced-by-count":16,"title":["Combinatorial properties of directed graphs useful in computing network reliability"],"prefix":"10.1002","volume":"11","author":[{"given":"A.","family":"Satyanarayana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jane N.","family":"Hagstrom","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","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho A. V.","year":"1974"},{"key":"e_1_2_1_3_2","unstructured":"A.SatyanarayanaandJ. N.Hagstrom \u201cA New Algorithm for the Reliability Analysis of Multi\u2010Terminal Networks \u201dIEEE Trans. Reliability to appear."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1978.5220266"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1979.5220585"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100107"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230110405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230110405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:47:17Z","timestamp":1699789637000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230110405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1981,12]]}},"alternative-id":["10.1002\/net.3230110405"],"URL":"https:\/\/doi.org\/10.1002\/net.3230110405","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1981,12]]}}}