Critical properties of the contact process on a scale-free homophilic network

Abstract

.Using the contact process model within a Monte Carlo numerical simulation approach, we mimic an epidemic spreading on a homophilic network, a scale-free network displaying a small world effect, to show a continuous phase transition to an absorbing-state at a critical threshold . Since the connection number k of the vertices’ homophilic network is cumulative, the degree distribution exhibits, for a large value of networks, a power-law behavior according to , with the distribution exponent . A finite-size scaling analysis allows us to characterize the transition by a set of critical exponents , , β and , whose universality class indicates a disagreement with those associated to the CP on scale-free networks in terms of the heterogeneous mean-field theory.