Assortative Mixing in Weighted Directed Networks

TL;DR

This paper introduces a new generalized assortativity coefficient for weighted directed networks, enabling detailed analysis of how vertices connect based on similarity, and provides statistical methods to assess its significance using real-world network data.

Contribution

It proposes a novel generalized assortativity coefficient for weighted networks and offers statistical procedures to evaluate assortativity significance.

Findings

The new coefficient captures connection and amplification effects in weighted networks.

Statistical methods effectively assess the significance of assortativity.

Application to real-world networks demonstrates the coefficient's utility.

Abstract

A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we propose to consider excess vertex strength, rather than excess degree, and show, that assortativity in weighted networks can be broken down into two mechanisms, which we refer to as the connection effect and the amplification effect. To capture these effects we introduce a generalised assortativity coefficient. This new coefficient allows for a more detailed interpretation and assessment of assortativity in weighted networks. Furthermore, we propose a procedure to assess the statistical significance of assortativity using jackknife, bootstrap and rewiring techniques. The usefulness of our proposed generalised assortativity coefficient is demonstrated by an in-depth analysis of the assortativity structure of several weighted real-world networks.