Degree-Degree Dependencies in Directed Networks with Heavy-Tailed Degrees

Q3 Mathematics Internet Mathematics Pub Date : 2013-10-24 DOI:10.1080/15427951.2014.927038
P. V. D. Hoorn, N. Litvak
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引用次数: 18

Abstract

In network theory, Pearson’s correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and out-degree sequences satisfy a power law with realistic parameters, Pearson’s correlation coefficients converge to a nonnegative number in the infinite network size limit. We propose alternative measures for degree-degree dependencies in directed networks based on Spearman’s rho and Kendall’s tau. Using examples and calculations on the Wikipedia graphs for nine different languages, we show why these rank correlation measures are more suited for measuring degree assortativity in directed graphs with heavy-tailed degrees.
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重尾度有向网络中的度-度依赖关系
在网络理论中,皮尔逊相关系数最常用于衡量网络的分类程度。我们研究了这些系数在重尾度序列有向网络设置中的行为。证明了对于进出度序列满足幂律的图,在无限网络规模极限下,Pearson相关系数收敛于一个非负数。我们提出了基于Spearman 's rho和Kendall 's tau的有向网络中度-度依赖的替代度量。通过对九种不同语言的维基百科图的示例和计算,我们展示了为什么这些排名相关度量更适合于测量具有重尾度的有向图中的度的协调性。
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Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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