Flow-based Community Detection in Hypergraphs

TL;DR

This paper compares two flow-based community detection methods, Markov stability and the map equation, applied to hypergraphs, analyzing their sensitivity to parameters and differences in community identification.

Contribution

It provides a detailed comparison of the machinery and performance of Markov stability and the map equation for hypergraph community detection.

Findings

Map equation is more sensitive to time-scale changes.

Markov stability is more sensitive to hyperedge-size biases.

Both methods reveal different community structures depending on parameters.

Abstract

To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and search algorithms. But how similar are the resulting communities? We explain both methods' machinery applied to hypergraphs and compare them on synthetic and real-world hypergraphs using various hyperedge-size biased random walks and time scales. We find that the map equation is more sensitive to time-scale changes and that Markov stability is more sensitive to hyperedge-size biases.