Hypergraph

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In mathematics, a hypergraph is a generalization of a graph
in which an edge can join any number of vertices.
In contrast, in an ordinary graph, an edge connects exactly two vertices.

A directed hypergraph differs in that its hyperedges are not sets,
but an ordered pair of subsets of X, constituting the tail and
head of the hyperedge.

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Hypergraphs can be viewed as incidence structures.

In particular, there is a bipartite "incidence graph" or "Levi graph"
corresponding to every hypergraph, and conversely,
most, but not all, bipartite graphs can be regarded as
incidence graphs of hypergraphs.