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

Pim van der Hoorn, Nelly Litvak

Published 2014-07-29, updated 2014-10-14Version 2

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.