  We introduce a clustering coefficient for nondirected and directed
hypergraphs, which we call the quad clustering coefficient. We determine the
average quad clustering coefficient and its distribution in real-world
hypergraphs and compare its value with those of random hypergraphs drawn from
the configuration model. We find that real-world hypergraphs exhibit a
nonnegligible fraction of nodes with a maximal value of the quad clustering
coefficient, while we do not find such nodes in random hypergraphs.
Interestingly, these highly clustered nodes can have large degrees and can be
incident to hyperedges of large cardinality. Moreover, highly clustered nodes
are not observed in an analysis based on the pairwise clustering coefficient of
the associated projected graph that has binary interactions, and hence higher
order interactions are required to identify nodes with a large quad clustering
coefficient.
