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Random walks have been intensively studied on regular and complex networks,which are used to represent pairwise interactions. Nonetheless, recent workshave demonstrated that many real-world processes are better captured byhigher-order relationships, which are naturally represented by hypergraphs.Here, we study random walks on hypergraphs. Due to the higher-order nature ofthese mathematical objects, one can define more than one type of walks. Inparticular, we study the unbiased and the maximal entropy random walk onhypergraphs, emphasizing their similarities and differences. We characterizethese processes through their stationary distributions and the associatedhitting times, which we obtain analytically. To illustrate our findings, wepresent a toy example and conduct extensive analyses of artificial and realhypergraphs, providing insights into both their structural and dynamicalproperties. We hope that our findings motivate further research extending theanalysis to different classes of random walks as well as to practicalapplications.

From unbiased to maximal entropy random walks on hypergraphs