{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T06:22:30Z","timestamp":1791267750136,"version":"4.1.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"A","license":[{"start":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T00:00:00Z","timestamp":1459296000000},"content-version":"unspecified","delay-in-days":485,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>Consider a random multigraph <jats:italic>G<\/jats:italic><jats:sup>*<\/jats:sup> with given vertex degrees <jats:italic>d<\/jats:italic><jats:sub>1<\/jats:sub>,\u2026, <jats:italic>d<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0021900200021239_inline1\"\/> the probability that the multigraph is simple stays away from 0 if and only if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0021900200021239_inline2\"\/> The new proof uses the method of moments, which makes it possible to use it in some applications concerning convergence in distribution. Corresponding results for bipartite graphs are included.<\/jats:p>","DOI":"10.1239\/jap\/1417528471","type":"journal-article","created":{"date-parts":[[2014,12,2]],"date-time":"2014-12-02T09:01:26Z","timestamp":1417510886000},"page":"123-137","source":"Crossref","is-referenced-by-count":29,"title":["The probability that a random multigraph is simple. II"],"prefix":"10.1017","volume":"51","author":[{"given":"Svante","family":"Janson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200021239_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009644"},{"key":"S0021900200021239_ref13","first-page":"225","volume-title":"Enumeration and Design (Waterloo, Ontario, 1982)","author":"McKay","year":"1984"},{"key":"S0021900200021239_ref17","unstructured":"[17] Wormald N. C. (1978). Some problems in the enumeration of labelled graphs. Doctoral Thesis, University of Newcastle."},{"key":"S0021900200021239_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80022-6"},{"key":"S0021900200021239_ref1","first-page":"343","article-title":"Asymptotic enumeration of regular matrices","volume":"7","author":"B\u00e9k\u00e9ssy","year":"1972","journal-title":"Studia Sci. Math. Hungar."},{"key":"S0021900200021239_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90059-6"},{"key":"S0021900200021239_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"S0021900200021239_ref16","volume-title":"NIST Handbook of Mathematical Functions","author":"Olver","year":"2010"},{"key":"S0021900200021239_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"S0021900200021239_ref6","unstructured":"[6] Bollob\u00e1s B. , and Riordan O. (2012). An old approach to the giant component problem. Preprint. Available at http:\/\/arxiv.org\/abs\/1209.3691v1."},{"key":"S0021900200021239_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"S0021900200021239_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.03.005"},{"key":"S0021900200021239_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4708-5"},{"key":"S0021900200021239_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP478"},{"key":"S0021900200021239_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20575"},{"key":"S0021900200021239_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20403"},{"key":"S0021900200021239_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01275671"},{"key":"S0021900200021239_ref14","first-page":"15","article-title":"Asymptotics for symmetric 0-1 matrices with prescribed row sums","volume":"19A","author":"McKay","year":"1985","journal-title":"Ars Combinatoria"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200021239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,21]],"date-time":"2019-04-21T18:33:02Z","timestamp":1555871582000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200021239\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":18,"aliases":["10.1017\/s0021900200021239"],"journal-issue":{"issue":"A","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200021239"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1417528471","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}