网络结点度相关性测度及其稳定性分析

判别网络同配/异配性的Newman相关系数r(g)和网络无标度程度的S(g)是研究网络结点度相关性的两个重要测度,其相关论文被科研人员广泛地引用,两个测度分别被应用到实际网络的同配/异配性和无标度程度的分析.为检验两个测度的稳定性,以BA模型为例,通过大量的计算机模拟和数值统计分析,结果显示:BA-3模型的r(g)与网络规模N的经验公式:r(g)∝-N-0.32,并指出r(g)和S(g)关于网络规模N、网络稠密度ρ都具有波动性.因此,用它们来分析不同规模或不同稠密度的有限的、增长的实际网络,其研究会产生一些误导性结果.

NETWORK NODE DEGREE CORRELATION METRICS WITH STABILITY ANALYSIS

Newman correlation coefficient r(g) for network assortative or disassortative mixing and S(g) for network scale-free degree are two important metrics to analyze the network node degree correlations.Their related papers are popularly quoted by researchers.Moreover the two metrics are respectively applied to practical networks’assortative or disassortative mixing and scale-free degree analysis.To test the stability of the two metrics,by taking BA model as an example,a lot of computer simulations and statistical analysis are carried out.The results demonstrate BA-3 model’s r(g) and network scale N’s empirical formula r(g)∝-N-0.32.Moreover,both r(g) and S(g) are fluctuant about network scale N and network dense degree ρ.Hence if they are used to analysis limited and growing practical networks of different sizes or different dense degrees,their studies may generate some misleading conclusions.