{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T16:44:38Z","timestamp":1773420278598,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given integers $n$ and $m=\\lfloor\\beta n \\rfloor$ and a probability measure $Q$ on $\\{0, 1,\\dots, m\\}$, consider the random intersection graph on the vertex set $[n]=\\{1,2,\\dots, n\\}$ where $i,j\\in [n]$ are declared adjacent whenever $S(i)\\cap S(j)\\neq\\emptyset$. Here $S(1),\\dots, S(n)$ denote the iid random subsets of $[m]$ with the distribution $\\bf{P}(S(i)=A)={{m}\\choose{|A|}}^{-1}Q(|A|)$,  $A\\subset [m]$. For sparse random intersection graphs,  we establish a first-order asymptotic as $n\\to \\infty$ for the order of the largest connected component $N_1=n(1-Q(0))\\rho+o_P(n)$. Here $\\rho$ is the average of   nonextinction probabilities of a related multitype Poisson branching process.<\/jats:p>","DOI":"10.37236\/382","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:10:50Z","timestamp":1578697850000},"source":"Crossref","is-referenced-by-count":10,"title":["The Largest Component in an Inhomogeneous Random Intersection Graph with Clustering"],"prefix":"10.37236","volume":"17","author":[{"given":"Mindaugas","family":"Bloznelis","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,8,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r110\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r110\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:28:02Z","timestamp":1579285682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/382","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,9]]},"article-number":"R110"}}