Effect of network topology on the ordering dynamics of voter models

TL;DR

This paper introduces the reverse voter model, a variation of the classic voter dynamics, analyzing how network topology influences the time to reach consensus, with analytical and numerical results on scale-free networks.

Contribution

The paper presents the reverse voter model and provides analytical and numerical analysis of its consensus time on scale-free networks, highlighting the impact of degree distribution.

Findings

Consensus time is linear in system size for degree exponent nu>2.

Reverse voter dynamics differ from traditional voter models in neighbor influence.

Results verified on uncorrelated scale-free graphs.

Abstract

We introduce and study the reverse voter model, a dynamics for spin variables similar to the well-known voter dynamics. The difference is in the way neighbors influence each other: once a node is selected and one among its neighbors chosen, the neighbor is made equal to the selected node, while in the usual voter dynamics the update goes in the opposite direction. The reverse voter dynamics is studied analytically, showing that on networks with degree distribution decaying as k^{-nu}, the time to reach consensus is linear in the system size N for all nu>2. The consensus time for link-update voter dynamics is computed as well. We verify the results numerically on a class of uncorrelated scale-free graphs.