Cycle and flow trusses in directed networks

TL;DR

This paper introduces a unified framework for identifying two distinct types of module structures, cycle and flow trusses, in directed networks, revealing their coexistence and potential for better network analysis.

Contribution

The authors propose a generic definition of truss structures in directed networks that captures both cycle and flow trusses within a single framework.

Findings

Most real-world directed networks contain both cycle and flow trusses.

The abundance and overlap of the two truss types help characterize network modules.

Considering multiple module types provides deeper insights into network structure.

Abstract

When we represent real-world systems as networks, the directions of links often convey valuable information. Finding module structures that respect link directions is one of the most important tasks for analyzing directed networks. Although many notions of a directed module have been proposed, no consensus has been reached. This lack of consensus results partly because there might exist distinct types of modules in a single directed network, whereas most previous studies focused on an independent criterion for modules. To address this issue, we propose a generic notion of the so-called truss structures in directed networks. Our definition of truss is able to extract two distinct types of trusses, named the cycle truss and the flow truss, from a unified framework. By applying the method for finding trusses to empirical networks obtained from a wide range of research fields, we find that most real networks contain both cycle and flow trusses. In addition, the abundance of (and the overlap between) the two types of trusses may be useful to characterize module structures in a wide variety of empirical networks. Our findings shed light on the importance of simultaneously considering different types of modules in directed networks.