Random walks and community detection in hypergraphs

TL;DR

This paper introduces a family of biased random walk processes on hypergraphs, linking them to hypergraph projections and community detection, and extends Markov stability for hypergraph analysis.

Contribution

It presents a novel one-parameter family of random walks on hypergraphs and generalizes community detection via Markov stability to hypergraph structures.

Findings

Different random walk biases reveal distinct community structures.

The framework works on both artificial and real-world hypergraphs.

Hypergraph projections vary with the bias parameter.

Abstract

We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by considering the community structure associated to each random walk process. To do so, we generalise the Markov stability framework to hypergraphs and test it on artificial and real-world hypergraphs.