Revising the simple measures of assortativity in complex networks

TL;DR

This paper introduces a revised measure for degree mixing in complex networks that accounts for superrich nodes, revealing more accurate mixing patterns and correcting previous misconceptions about network disassortativity.

Contribution

The authors propose a new paradigm and simple measure to accurately assess degree mixing patterns in networks with superrich nodes, overcoming limitations of traditional statistics.

Findings

Traditional measures are affected by superrich nodes.

Some networks are falsely identified as disassortative.

Superrich nodes exacerbate network fragility.

Abstract

We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low-degree nodes and among high-degree nodes. The new paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes. The new method indicates that some networks show a false disassortative mixing induced by superrich nodes, and have no tendency to be genuinely disassortative. Our results also show that the previously observed fragility of scale-free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes.