{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822845,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Rado Graph, sometimes also known as the (countable) Random Graph, can be generated almost surely by putting an edge between any pair of vertices with some fixed probability $p\\in(0,1)$, independently of other pairs.\r\nIn this article, we study the influence of allowing different probabilities for each pair of vertices. More specifically, we characterize for which sequences $(p_n)_{n\\in \\mathbb{N}}$ of values in $[0,1]$ there exists a bijection $f$ from pairs of vertices in $\\mathbb{N}$ to $\\mathbb{N}$ such that if we put an edge between $v$ and $w$ with probability $p_{f(\\{v,w\\})}$, independently of other pairs, then the Random Graph arises almost surely.<\/jats:p>","DOI":"10.37236\/12960","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T18:33:31Z","timestamp":1749148411000},"source":"Crossref","is-referenced-by-count":0,"title":["How to Get the Random Graph with Non-Uniform Probabilities?"],"prefix":"10.37236","volume":"32","author":[{"given":"Leonardo","family":"Coregliano","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaros\u0142aw","family":"Swaczyna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agnieszka","family":"Widz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,6,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T18:33:31Z","timestamp":1749148411000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/12960","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,6,6]]},"article-number":"P2.45"}}