Hypergraph

A hypergraph is a generalization of a graph in which a single edge, called a hyperedge, can join any number of vertices rather than exactly two as in an ordinary graph. Formally, an undirected hypergraph is a pair consisting of a vertex set and a collection of subsets of that vertex set serving as its hyperedges, while a directed hypergraph pairs each hyperedge with a tail and a head, each itself a subset of vertices. Hypergraphs can be viewed as incidence structures: every hypergraph corresponds to a bipartite incidence graph, and conversely every bipartite graph can be read as the incidence graph of some hypergraph. The concept appears under other names in other fields, called a range space in computational geometry and a simple game or voting game in cooperative game theory.