  A hypergraph is a useful combinatorial object to model ternary or
higher-order relations among entities. Clustering hypergraphs is a fundamental
task in network analysis. In this study, we develop two clustering algorithms
based on personalized PageRank on hypergraphs. The first one is local in the
sense that its goal is to find a tightly connected vertex set with a bounded
volume including a specified vertex. The second one is global in the sense that
its goal is to find a tightly connected vertex set. For both algorithms, we
discuss theoretical guarantees on the conductance of the output vertex set.
Also, we experimentally demonstrate that our clustering algorithms outperform
existing methods in terms of both the solution quality and running time. To the
best of our knowledge, ours are the first practical algorithms for hypergraphs
with theoretical guarantees on the conductance of the output set.
