Voter Model on Heterogeneous Graphs
Abstract
We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T_{N} scales as Nμ^{2}_{1}/μ_{2}, where μ_{k} is the kth moment of the degree distribution. For a powerlaw degree distribution n_{k}∼k^{ν}, T_{N} thus scales as N for ν>3, as N/ln(N for ν=3, as N^{(2ν4)/(ν1)} for 2<ν<3, as (ln(N)^{2} for ν=2, and as O(1) for ν<2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.
 Publication:

Physical Review Letters
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevLett.94.178701
 arXiv:
 arXiv:condmat/0412599
 Bibcode:
 2005PhRvL..94q8701S
 Keywords:

 89.75.Fb;
 02.50.r;
 05.40.a;
 Structures and organization in complex systems;
 Probability theory stochastic processes and statistics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 4 pages, 4 figures, 2column revtex4 format. Version 2 has been revised somewhat to account for referee comments. To appear in PRL