Voter Model on Heterogeneous Graphs

Details Voter Model on Heterogeneous Graphs Voter Model on Heterogeneous Graphs

2004-12-22

arxiv.org/abs/cond-mat/0412599v2

Phys. Rev. Lett. 94, 178701 (2005).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, 2-column revtex4 format. Version 2 has been revised somewhat to account for referee comments. To appear in

Scientific paper

10.1103/PhysRevLett.94.178701

We study the voter dynamics model on heterogeneous graphs. We exploit the non-conservation of the magnetization to characterize how consensus is reached on networks with different connectivity patterns. For a network of N sites with an arbitrary degree distribution, we show that the mean time to reach consensus T_N scales as N mu_1^2/mu_2, where mu_k is the kth moment of the degree distribution. For a power-law degree distribution n_k k^{-nu}, we thus find that T_N scales as N for nu>3, as N/ln N for nu=3, as N^{(2nu-4)/(nu-1)} for 2

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