Compression of Flow Can Reveal Overlapping-Module Organization in Networks

TL;DR

This paper introduces an information-theoretic method called the map equation for overlapping modules, enabling the detection of complex, overlapping community structures in large flow networks by optimizing network compression.

Contribution

It presents a novel generalized map equation and a greedy algorithm to identify overlapping modules that best describe flow in networks, advancing network community detection methods.

Findings

Neural network of C. Elegans has modules with hard boundaries.

European road network exhibits highly overlapping modular organization.

The method effectively captures flow-based community structures.

Abstract

To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between compression and regularity detection. The generalized map equation measures how well we can compress a description of flow in the network when we partition it into modules with possible overlaps. When we minimize the generalized map equation over overlapping network partitions, we detect modules that capture flow and determine which nodes at the boundaries between modules should be classified in multiple modules and to what degree. With a novel greedy search algorithm, we find that some networks, for example, the neural network of C. Elegans, are best described by modules dominated by hard boundaries, but that others, for example, the sparse European road network, have a highly overlapping modular organization.