Mapping flows on hypergraphs

TL;DR

This paper develops methods to map and analyze flow dynamics on hypergraphs, providing new representations and community detection techniques to understand multibody interactions in complex systems.

Contribution

It introduces unipartite, bipartite, and multilayer network models for hypergraph flows, enhancing community detection and understanding of multibody interactions.

Findings

Different network representations affect community detection results.

The models reveal how flow structures vary with hypergraph topology.

Guidelines for choosing appropriate models for flow mapping.

Abstract

Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. But mapping the large-scale structure of those flows requires effective community detection methods. We derive unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.