On some combinatorial properties of random intersection graphs

Abstract

In this paper, we consider a simple, yet general family of random graph models, namely Random Intersection Graphs (RIGs), which are motivated by applications in secure sensor networks, social networks and many more. In such models there is a universe M of labels and each one of n vertices selects a random subset of M. Two vertices are connected if and only if their corresponding subsets of labels intersect. In particular, we briefly review the state of the art and we present key results from our research on the field, that highlight and take advantage of the intricacies and special structure of random intersection graphs. Finally, we present in more detail a particular result from our research, which concerns maximum cliques in the uniform random intersection graphs model (in which every vertex selects each label independently with some probability p), namely the Single Label Clique Theorem.