%0 Journal Article %1 Sood2005 %A Sood, V. %A Redner, S. %D 2005 %I American Physical Society %J Physical Review Letters %K graphs networks opinion-formation voter-model %N 17 %P 178701+ %R 10.1103/PhysRevLett.94.178701 %T Voter Model on Heterogeneous Graphs %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{Sood2005, 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 = {2011-03-14T17:14:06.000+0100}, author = {Sood, V. and Redner, S.}, biburl = {https://www.bibsonomy.org/bibtex/24afb384756e2a6f4d3b35eee646a8a02/rincedd}, day = 3, doi = {10.1103/PhysRevLett.94.178701}, interhash = {4c57440ae015a6e94e23249bb034ce19}, intrahash = {4afb384756e2a6f4d3b35eee646a8a02}, journal = {Physical Review Letters}, keywords = {graphs networks opinion-formation voter-model}, month = may, number = 17, pages = {178701+}, publisher = {American Physical Society}, timestamp = {2011-03-14T17:14:07.000+0100}, title = {Voter Model on Heterogeneous Graphs}, volume = 94, year = 2005 }