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., $O\left(N\right)$] and a slow consensus regime [i.e., $O\left(N^2\right)$], 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 $O\left(1\right)$ interclique links. The present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited.

• Received 19 March 2014

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©2014 American Physical Society