Edge direction and the structure of networks

TL;DR

This paper explores how edge direction influences assortativity in directed networks, revealing complex patterns and limitations of existing models across various network types.

Contribution

It introduces four directed assortativity measures, demonstrating their effectiveness in analyzing diverse networks and challenging the traditional binary classification.

Findings

Edge direction significantly impacts assortativity patterns.

Directed networks exhibit mixed assortative and disassortative features.

Existing models often fail to capture the complexity of directed network assortativity.

Abstract

Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it has been disregarded in studying a basic type of global diversity in networks: the tendency of nodes with similar numbers of edges to connect. This tendency, called assortativity, affects crucial structural and dynamic properties of real-world networks, such as error tolerance or epidemic spreading. Here we demonstrate that edge direction has profound effects on assortativity. We define a set of four directed assortativity measures and assign statistical significance by comparison to randomized networks. We apply these measures to three network classes---online/social networks, food webs, and word-adjacency networks. Our measures (i) reveal patterns common to each class, (ii) separate networks that have been previously classified together, and (iii) expose limitations of several existing theoretical models. We reject the standard classification of directed networks as purely assortative or disassortative. Many display a class-specific mixture, likely reflecting functional or historical constraints, contingencies, and forces guiding the system's evolution.