Voter Model on Heterogeneous Graphs.

We study basic properties of the voter model on heterogeneous graphs with an arbitrary degree distribution. By mapping the voter model to a coalescing random walk, we are able to understand the effect of the degree distribution on the dynamical behavior. We thereby find that the mean consensus time for finite graphs of $N$ sites scales as $\mu_1^2 N/\mu_2$, where $\mu_1$ is the mean degree and $\mu_2$ the second moment of the degree distribution. Thus the consensus time may scale sublinearly with system size if the degree distribution is sufficiently broad.