{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T13:00:48Z","timestamp":1776430848334,"version":"3.51.2"},"reference-count":12,"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":4485,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1994,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the reliability of graphs for which nodes fail independently of each other with a constant probability 1 \u2010<jats:italic>p<\/jats:italic>. The reliability of a graph is defined to be the probability that the induced subgraph of surviving nodes is connected. A graph is said to be uniformly best when, for all choices of<jats:italic>p<\/jats:italic>, it is most reliable in the class of graphs with the same number of nodes and same number of edges. In this paper, we first extend the existing known set of uniformly best graphs. Next, we show that most classes of sparse graphs do not contain a uniformly best graph. Finally, we introduce the important notions of locally best and asymptotically best graphs and illustrate these concepts with a detailed study of graphs having the same number of nodes and edges. \u00a9 1994 by John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/net.3230240407","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T18:22:08Z","timestamp":1178994128000},"page":"251-259","source":"Crossref","is-referenced-by-count":30,"title":["On reliability of graphs with node failures"],"prefix":"10.1002","volume":"24","author":[{"given":"Olivier","family":"Goldschmidt","sequence":"first","affiliation":[]},{"given":"Patrick","family":"Jaillet","sequence":"additional","affiliation":[]},{"given":"Richard","family":"Lasota","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0120023"},{"key":"e_1_2_1_3_2","unstructured":"F.Boesch A.Satyanarayana andC.Suffel On residual connectedness network reliability. Preprint Stevens Institute of Technology (1990). Presented at ORSA\/TIMS."},{"key":"e_1_2_1_4_2","volume-title":"Random Graphs","author":"Bollobas B.","year":"1985"},{"key":"e_1_2_1_5_2","volume-title":"The Combinatories of Network Reliability","author":"Colbourn C.","year":"1987"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(93)90233-E"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230190106"},{"key":"e_1_2_1_8_2","unstructured":"O.Goldschmidt P.Jaillet andR.LaSota Node reliability results. Joint technical Report of the Dept. of Mechanical Engineering and the MSIS Dept. University of Texas at Austin (1992)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230030304"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198533863.001.0001","volume-title":"Network Reliability and Algebraic Structures","author":"Shier D. R.","year":"1991"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230140105"},{"key":"e_1_2_1_12_2","unstructured":"C.Stivaros On the residual node connectedness network reliability model. PhD Dissertation Dept. of Electrical Engineering and Computer Science Stevens Institute of Technology (1990)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0220009"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230240407","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230240407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T06:51:26Z","timestamp":1707893486000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230240407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,7]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,7]]}},"alternative-id":["10.1002\/net.3230240407"],"URL":"https:\/\/doi.org\/10.1002\/net.3230240407","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,7]]}}}