Kernel nonlinearity in heterogeneous evolving networks

Abstract

In this paper we present an analysis of the interplay between kernel nonlinearity and heterogeneity in preferential attachment (PA) based network models. We define an extended class of heterogeneous PA models where the attachment kernel is a nonlinear function of the connectivity degree of the existing network nodes. Like the original class of heterogeneous PA models, the attachment kernel is also biased by the affinity between the states of pairs of nodes involved in a potential interaction. We show that the class of models exhibit four kinetic regimes in their degree connectivities which are robust against the form of heterogeneity and low-level details of the functional form of the attachment kernel.