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

TL;DR

This paper introduces and analyzes three rank-based measures for degree-degree correlations in directed networks, demonstrating their statistical consistency and advantages over Pearson's correlation, especially in large scale-free networks.

Contribution

The paper proposes new rank-based dependency measures for directed networks and proves their consistency, offering a robust alternative to Pearson's correlation in complex network analysis.

Findings

Rank-based measures are statistically consistent in random graphs.

Directed configuration model serves as an effective null model.

Rank-based measures outperform Pearson's correlation in large scale-free 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.