Emergence of the giant component in preferential-attachment growing networks

Abstract

We study the percolation transition in evolving scale-free networks. A new node is added at each step and is connected to a random number of old nodes according to the preferential attachment mechanism. We give the critical value of the emergence of the giant component and prove that the transition is of infinite order. We also obtain asymptotic expressions for the cluster size distribution in the subcritical, critical, and supercritical regimes.