The noisy voter model on complex networks

TL;DR

This paper introduces an analytical method to study stochastic binary-state models on complex networks, accounting for network heterogeneity, and applies it to the noisy voter model to reveal how degree variance influences critical behavior and correlations.

Contribution

The paper develops an annealed approximation approach that incorporates degree heterogeneity into the analysis of stochastic models on networks, extending beyond mean-field theories.

Findings

Degree heterogeneity significantly affects the critical point of the transition.

The model's temporal correlations depend on the degree distribution.

Network heterogeneity can be inferred from aggregate system behavior.

Abstract

We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity ---variance of the underlying degree distribution--- has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.