Activity maxima in random networks in the heavy tail case

Abstract

We consider a model of information network described by an undirected random graph, where each node has a random information activity whose distribution possesses a heavy tail (with regular variation). We investigate the cases of networks described by classical and power-law random graphs. We derive sufficient conditions under which the maximum of aggregate activities (over a node and its nearest neighbors) asymptotically grows in the same way as the maximium of individual activities and the Frechet limit law holds for them.