%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/ln⁡N for ν=3, as N(2ν-4)/(ν-1) 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.

@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/ln⁡N for ν=3, as N(2ν-4)/(ν-1) 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.}}, 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 }