Flow-based community detection in hypergraphs

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.