Heterogeneous pair approximation for voter models on networks

TL;DR

This paper introduces a heterogeneous pair approximation method for voter models on networks, providing a more accurate and general description of the dynamics by incorporating degree dependence, improving upon previous mean-field approaches.

Contribution

The paper develops a heterogeneous pair approximation for voter models, enhancing the accuracy of network dynamics analysis by explicitly including degree dependence.

Findings

Provides an essentially exact description of voter model dynamics on uncorrelated networks.

Corrects inaccuracies of previous approximation methods.

Applicable to a wide range of processes on complex networks.

Abstract

For models whose evolution takes place on a network it is often necessary to augment the mean-field approach by considering explicitly the degree dependence of average quantities (heterogeneous mean-field). Here we introduce the degree dependence in the pair approximation (heterogeneous pair approximation) for analyzing voter models on uncorrelated networks. This approach gives an essentially exact description of the dynamics, correcting some inaccurate results of previous approaches. The heterogeneous pair approximation introduced here can be applied in full generality to many other processes on complex networks.