增长网络结点度相关性的混合系数

A Mixing Coefficient for Node Degree Correlation in Growing Networks

鉴于增长网络的一个显著特征是相邻结点之间的关系自发地形成,与被广泛研究的结点度分布相比,此种相邻结点关系的研究能更清楚地揭示更多内在的增长网络的结构特征.为此提出了一种称为混合系数M(g)的网络结点度相关性测度用来判别增长网络的同配和异配性.通过大量的计算机模拟和数值统计,分析了该测度关于网络规模N和稠密度ρ的稳定性,结果显示该测度比判别网络同配和异配性的Newman相关系数r(g)更具有稳定性.因此,混合系数M(g)具有优越性,可更好地被应用到实际网络的同配和异配性分析中.

A notable feature of growing networks is the spontaneous forming of the relationship among adjacent nodes. Compared with the widely studied node degree distribution, the research on relationship between adjacent nodes can lead to finding more internal features in growing networks. This paper puts forward a mixing coefficient M（g） for the node degree correlation in growing networks, which can be used to measure the assortative and disassortative mixing. Through a given number of computer simulations and numerical statistic samplings, this paper studies the stability concerning network＇s size and density degree. The result shows that the metric is more stable in terms of network＇s size and density degree than Newman correlation coefficient r（g）. It concludes that the mixing coefficient M（g） can be effectively applied to the assortative and disassortative mixing analysis in physical networks.