Mean-field analysis of the q-voter model on networks

TL;DR

This paper provides a comprehensive mean-field analysis of the q-voter model on networks, deriving phase diagrams, exit probabilities, and consensus times, and extends the analysis to heterogeneous and regular networks with simulation comparisons.

Contribution

It introduces an analytical mean-field framework for the q-voter model applicable to various network types, including heterogeneous and regular networks, with validation against simulations.

Findings

Analytical phase diagram and consensus time at transition point

Extension of mean-field formalism to heterogeneous networks

Agreement between analytical results and simulations on regular networks

Abstract

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.