Generalized voter-like models on heterogeneous networks

Abstract

This Chapter presents a generalized model of consensus formation, which is able to encompass all previous formulations of copy/invasion processes inspired by variations on the voter model and the Moran process. It considered the implementation of such generalized dynamics on a heterogeneous contact pattern, represented by a complex network, and derived the theoretical predictions for the relevant dynamical quantities, within the assumptions of the heterogeneous mean-field theory. The chapter provides a brief review of previous results that can be recovered by this generalized formalism, and considers a novel application to the case of opinion formation in a social network. In particular, it addressed the case in which the opinion strength of an individual is related to his/her degree centrality in the network. It has been that in scale-free networks strong selectivity rules (which make less connected individuals much more prone to change their opinions than more-connected ones or vice versa) lead to a steeper growth of consensus time with the system size, making the ordering process slower in general. Numerical simulations on quenched networks show that the HMF theory is able to predict such behavior with reasonable accuracy. Slight deviations from the theoretical predictions are encountered in certain regions of the phase diagram, but they are due to quenched-network effects that the HMF theory is not be able to capture.