Convergence of rank based degree-degree correlations in random directed networks

Abstract

We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman's rho and Kendall's tau. We proof statistical consistency of these measures in general random graphs and show that the directed configuration model can serve as a null model for our degree-degree dependency measures. Based on these results we argue that the measures we introduce should be preferred over Pearson's correlation coefficients, when studying degree-degree dependencies, since the latter has several issues in the case of large networks with scale-free degree distributions.

References in corpus (6)

• Assortative mixing in networks
• Mixing patterns in networks
• The origin of degree correlations in the Internet and other networks
• Uncovering disassortativity in large scale-free networks
• Degree-degree correlations in random graphs with heavy-tailed degrees
• Degree-degree dependencies in directed networks with heavy-tailed degrees