Voter model on heterogeneous graphs
Voter model on heterogeneous graphs
复制标题
DOI：
10.1103/physrevlett.94.178701
复制
发表时间：
2005-05-06
影响因子：
8.6
通讯作者：
Redner, S
中科院分区：
文献类型：
--
作者：
Sood, V;Redner, S
研究了异质图上的投票模型。我们利用磁化的不守恒来描述如何达成共识。对于一个具有任意但不相关度分布的N个节点的网络，达到共识的平均时间T-N标度为Nμ（2）（1）/μ（2），其中μ（k）是度分布的k阶矩。对于幂律度分布n（k）<$k（-ν），T-N因此对于ν 3为N，对于ν=3为N/lnN，对于2 ν 3为N（2ν-4）/（ν-1），对于ν=2为（lnN）（2），对于ν 2为O（1）。这些结果同意与网络的模拟数据与不相关和相关的节点度。
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 power-law degree distribution n(k)∼ k(-ν), T-N 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.