A Generalized Voter Model on Complex Networks

A generalization of the voter model on complex networks, focusing on the scaling of mean exit time, is studied and it is found that on a complete bipartite network, the Voter model is the fastest process.

Abstract

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