Analysis and perturbation of degree correlation in complex networks

TL;DR

This paper analytically investigates degree correlation in complex networks, revealing a linear relation and analyzing how structural perturbations affect assortativity differently in homogeneous and heterogeneous networks.

Contribution

It provides an exact proof of statistical measure consistency, uncovers a general linear relation in degree correlation, and studies the impact of structural perturbations on network assortativity.

Findings

Homogeneous networks are more sensitive to structural changes.

Degree correlation measures are consistent and follow a linear relation.

Perturbations significantly affect assortativity in ER graphs but less in scale-free networks.

Abstract

Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof of the consistency for the statistical measures, reveal the general linear relation in the degree correlation, which provide a simple and interesting perspective on the analysis of the degree correlation in complex networks. By using the general linear analysis, we investigate the perturbation of the degree correlation in complex networks caused by the addition of few nodes and the rich club. The results show that the assortativity of homogeneous networks such as the ER graphs is easily to be affected strongly by the simple structural changes, while it has only slight variation for heterogeneous networks with broad degree distribution such as the scale-free networks. Clearly, the homogeneous networks are more sensitive for the perturbation than the heterogeneous networks.