Voter model on the two-clique graph

Abstract

I examine the mean consensus time (i.e., exit time) of the voter model in the so-called two-clique graph. The two-clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks. I analytically show that, as the number of interclique links per node is varied, the mean consensus time experiences a crossover between a fast consensus regime [i.e., O(N)] and a slow consensus regime [i.e., O(N^2)], where N is the number of nodes. The fast regime is consistent with the result for homogeneous well-mixed graphs such as the complete graph. The slow regime appears only when the entire network has O(1) interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.

4 figures

References in corpus (12)

• Statistical physics of social dynamics
• Diffusion dynamics on multiplex networks
• Voter Models on Heterogeneous Networks
• Conservation laws for the voter model in complex networks
• Majority Model on a network with communities
• Fixation and consensus times on a network: a unified approach
• Anomalous lifetime distributions and topological traps in ordering dynamics
• Population genetics on islands connected by an arbitrary network: An analytic approach
• Broad lifetime distributions for ordering dynamics in complex networks
• Mass Media Influence Spreading in Social Networks with Community Structure
• Phase of Ising spins on modular networks analogous to social polarization
• Effects of mobility on ordering dynamics

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• Voter model on networks partitioned into two cliques of arbitrary sizes
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