Modularity of Directed Networks: Cycle Decomposition Approach

TL;DR

This paper introduces a novel cycle decomposition approach for directed networks that leverages random walks to identify fuzzy modules, preserving directional information and revealing functional subunits.

Contribution

It presents a new method combining cycle decomposition and random walks to detect modules in directed, weighted networks while maintaining directional information.

Findings

Cycle decomposition connects network modules and information transport.

The proposed measure captures directional information in a symmetric way.

The communication graph inherits modular structure from the original directed network.

Abstract

The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarse-grained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. walk process, for which we will prove that although being time-reversible it inherits all necessary information about directions and modular structure of the original network. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.