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Zbl 1042.05091
Stark, Dudley
The vertex degree distribution of random intersection graphs. (English)
[J] Random Struct. Algorithms 24, No. 3, 249-258 (2004). ISSN 1042-9832; ISSN 1098-2418/e

Summary: Random intersection graphs are a model of random graphs in which each vertex is assigned a subset of a set of objects independently and two vertices are adjacent if their assigned subsets are not disjoint. The number of vertices is denoted by $n$ and the number of objects is supposed to be $\lfloor n^{\alpha} \rfloor$ for some $\alpha > 0$. We determine the distribution of the degree of a typical vertex and show that it changes sharply between $\alpha > 1$, $\alpha = 1$, and $\alpha< 1$.

MSC 2000:: *05C80 Random graphs

Keywords: random graphs

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Zentralblatt MATH Berlin [Germany]