  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.
