A hypergraph is a generalization of a graph in which an edge can connect any number of vertices, rather than just two. In a traditional graph, an edge is a connection between exactly two vertices. In contrast, a hypergraph allows an edge (often called a hyperedge) to link multiple vertices simultaneously.
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A hypergraph consists of a vertex set and a collection of subsets of , called hyperedges. In a simple hypergraph the collection has no repeated member. A uniform hypergraph restricts every hyperedge to a fixed size ; ordinary simple graphs are the case .
For example, on the edges and form a 3-uniform hypergraph. Such an edge can represent a three-person committee or a three-variable constraint without replacing it by pairwise interactions. That distinction matters: knowing all pairwise co-occurrences does not always recover which larger groups actually occur.