Central Limit Theorem for the Largest Component of Random Intersection Graph

Abstract

Random intersection graphs are models of random graphs in which each vertex is assigned a subset of objects independently and two vertices are adjacent if their assigned subsets are adjacent. Let $n$ and $m=[\beta n^{\alpha}]$ denote the number of vertices and objects respectively. We get a central limit theorem for the largest component of the random intersection graph $G(n,m,p)$ in the supercritical regime and show that it changes between $\alpha>1$, $\alpha=1$ and $\alpha<1$.