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Voter Model on Heterogeneous Graphs

V. Sood·S. Redner
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Abstract

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<nu<3, as (ln N)^2 for nu=2, and as order one for nu<2.

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BibTeXRIS

V. Sood, S. Redner. 2005-04-03. Voter Model on Heterogeneous Graphs. https://doi.org/10.1103/physrevlett.94.178701

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