Central Limit Theorem for the Largest Component of Random Intersection Graph

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.