Mapping flows on hypergraphs

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.