Component Evolution in Random Intersection Graphs

Abstract

We study the evolution of the order of the largest component in the random intersection graph model which reflects some clustering properties of real–world networks. We show that for appropriate choice of the parameters random intersection graphs differ from $G_{n,p}$ in that neither the so-called giant component, appearing when the expected vertex degree gets larger than one, has linear order nor is the second largest of logarithmic order. We also describe a test of our result on a protein similarity network.