Voter Model on Heterogeneous Graphs
Statistical Mechanics
2009-11-10 v2 Physics and Society
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.
Keywords
Cite
@article{arxiv.cond-mat/0412599,
title = {Voter Model on Heterogeneous Graphs},
author = {V. Sood and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/0412599},
year = {2009}
}
Comments
4 pages, 4 figures, 2-column revtex4 format. Version 2 has been revised somewhat to account for referee comments. To appear in PRL