{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T22:12:48Z","timestamp":1785017568740,"version":"3.55.0"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T00:00:00Z","timestamp":1368662400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:p>Every graphon defines a random graph on any given number <jats:italic>n<\/jats:italic> of vertices. It was known that the graphon is random-free if and only if the entropy of this random graph is subquadratic. We prove that for random-free graphons, this entropy can grow as fast as any subquadratic function. However, if the graphon belongs to the closure of a random-free hereditary graph property, then the entropy is <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic> log <jats:italic>n<\/jats:italic>). We also give a simple construction of a non-step-function random-free graphon for which this entropy is linear, refuting a conjecture of Janson.<\/jats:p>","DOI":"10.1017\/s0963548313000175","type":"journal-article","created":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T08:55:22Z","timestamp":1368694522000},"page":"517-526","source":"Crossref","is-referenced-by-count":10,"title":["The Entropy of Random-Free Graphons and Properties"],"prefix":"10.1017","volume":"22","author":[{"given":"HAMED","family":"HATAMI","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"SERGUEI","family":"NORINE","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,5,16]]},"reference":[{"key":"S0963548313000175_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.05.002"},{"key":"S0963548313000175_ref3","volume-title":"Extremal Graph Theory, Vol. 11 of London Mathematical Society Monographs","author":"Bollob\u00e1s","year":"1978"},{"key":"S0963548313000175_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/050627915"},{"key":"S0963548313000175_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099420"},{"key":"S0963548313000175_ref5","unstructured":"Hatami H. , Janson S. and Szegedy B. Graph properties, graph limits and entropy. In preparation."},{"key":"S0963548313000175_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14444-8_12"},{"key":"S0963548313000175_ref6","unstructured":"Janson S. Graphons, cut norm and distance, couplings and rearrangements. arXiv:1009.2376"},{"key":"S0963548313000175_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-010-0044-0"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548313000175","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T21:15:22Z","timestamp":1556054122000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548313000175\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,16]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["S0963548313000175"],"URL":"https:\/\/doi.org\/10.1017\/s0963548313000175","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,16]]}}}