A generalized voter model on complex networks

TL;DR

This paper introduces a generalized voter model on complex networks, analyzing how different interaction rules and network structures influence the time it takes for the system to reach consensus.

Contribution

It proposes a new two-step process for the voter model that accounts for degree-based influence, extending traditional models and analyzing its effects on various network types.

Findings

Traditional voter model is fastest on complete bipartite networks.

Exit time depends on influence parameter and network degree distribution.

Different regimes of exit time behavior are identified based on influence strength.

Abstract

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter $\alpha$ which sets the likelihood of the higher degree node giving its state. Traditional voter model behavior can be recovered within the model. We find that on a complete bipartite network, the traditional voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of $\alpha$, exit time is dominated by diffusive drift of the system state, but as the high nodes become more influential, the exit time becomes becomes dominated by frustration effects. For certain selection processes, a short intermediate regime occurs where exit occurs after exponential mixing.