%0 Journal Article %1 sood:178701 %A Sood, V. %A Redner, S. %D 2005 %I APS %J Physical Review Letters %K RMP_CFL redner sood voter 2005 %N 17 %P 178701 %T Voter Model on Heterogeneous Graphs %U http://link.aps.org/abstract/PRL/v94/e178701 %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-nu, TN thus scales as N for nu>3, as N/lnN for nu=3, as N(2nu-4)/(nu-1) for 2<nu<3, as (lnN)2 for nu=2, and as script O(1) for nu<2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.

@article{sood:178701, 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-nu, TN thus scales as N for nu>3, as N/lnN for nu=3, as N(2nu-4)/(nu-1) for 2<nu<3, as (lnN)2 for nu=2, and as [script O](1) for nu<2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.}, added-at = {2006-12-19T11:10:08.000+0100}, author = {Sood, V. and Redner, S.}, biburl = {https://www.bibsonomy.org/bibtex/24afb384756e2a6f4d3b35eee646a8a02/vittorio.loreto}, eid = {178701}, interhash = {4c57440ae015a6e94e23249bb034ce19}, intrahash = {4afb384756e2a6f4d3b35eee646a8a02}, journal = {Physical Review Letters}, keywords = {RMP_CFL redner sood voter 2005}, number = 17, numpages = {4}, pages = 178701, publisher = {APS}, timestamp = {2006-12-19T11:10:08.000+0100}, title = {Voter Model on Heterogeneous Graphs}, url = {http://link.aps.org/abstract/PRL/v94/e178701}, volume = 94, year = 2005 }