Measuring degree-degree association in networks

TL;DR

This paper evaluates various measures for degree-degree association in complex networks, finding Kendall-Gibbons' tau_b to be more robust than Pearson's coefficient, especially for heavy-tailed degree distributions.

Contribution

It provides a probabilistic framework and comparative analysis showing the limitations of Pearson's coefficient and the robustness of Kendall-Gibbons' tau_b for network degree correlations.

Findings

Pearson's coefficient depends on network size for equal association structures.

Kendall-Gibbons' tau_b is more stable across different network sizes.

Heavy-tailed degree distributions challenge traditional correlation measures.

Abstract

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' $\tau_{b}$ is a considerably more robust measure of the degree-degree association.