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 TN scales as Nμ12/μ2, where μk is the kth moment of the degree distribution. For a power-law degree distribution nk∼k-ν, TN thus scales as N for ν>3, as N/lnN for ν=3, as N(2ν-4)/(ν-1) for 2<ν<3, as (lnN)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.
%0 Journal Article
%1 Sood2005Voter
%A Sood, V.
%A Redner, S.
%D 2005
%I American Physical Society
%J Physical Review Letters
%K voter-model scale-free-networks
%N 17
%P 178701+
%R 10.1103/physrevlett.94.178701
%T Voter Model on Heterogeneous Graphs
%U http://dx.doi.org/10.1103/physrevlett.94.178701
%V 94
%X 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 TN scales as Nμ12/μ2, where μk is the kth moment of the degree distribution. For a power-law degree distribution nk∼k-ν, TN thus scales as N for ν>3, as N/lnN for ν=3, as N(2ν-4)/(ν-1) for 2<ν<3, as (lnN)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.
@article{Sood2005Voter,
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 TN scales as Nμ12/μ2, where μk is the kth moment of the degree distribution. For a power-law degree distribution nk∼k-ν, TN thus scales as N for ν>3, as N/lnN for ν=3, as N(2ν-4)/(ν-1) for 2<ν<3, as (lnN)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.}},
added-at = {2019-06-10T14:53:09.000+0200},
archiveprefix = {arXiv},
author = {Sood, V. and Redner, S.},
biburl = {https://www.bibsonomy.org/bibtex/24afb384756e2a6f4d3b35eee646a8a02/nonancourt},
citeulike-article-id = {432244},
citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0412599},
citeulike-linkout-1 = {http://arxiv.org/pdf/cond-mat/0412599},
citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevlett.94.178701},
citeulike-linkout-3 = {http://link.aps.org/abstract/PRL/v94/i17/e178701},
citeulike-linkout-4 = {http://link.aps.org/pdf/PRL/v94/i17/e178701},
day = 3,
doi = {10.1103/physrevlett.94.178701},
eprint = {cond-mat/0412599},
interhash = {4c57440ae015a6e94e23249bb034ce19},
intrahash = {4afb384756e2a6f4d3b35eee646a8a02},
journal = {Physical Review Letters},
keywords = {voter-model scale-free-networks},
month = may,
number = 17,
pages = {178701+},
posted-at = {2012-11-15 12:19:10},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-08-01T16:13:16.000+0200},
title = {{Voter Model on Heterogeneous Graphs}},
url = {http://dx.doi.org/10.1103/physrevlett.94.178701},
volume = 94,
year = 2005
}