(data structure)

Definition: A graph whose hyperedges connect two or more vertices.

Formal Definition: A hypergraph G can be defined as a pair (V, E), where V is a set of vertices, and E is a set of hyperedges between the vertices. Each hyperedge is a set of vertices: E ⊆ {{u, v, ...} ∈ 2V}. (Hyperedges are undirected.)

Generalization (I am a kind of ...)
undirected graph.

Aggregate child (... is a part of or used in me.)
hyperedge, vertex.

See also multigraph.

Note: Consider "family," a relation connecting two or more people. If each person is a vertex, a family hyperedge connects the father, the mother, and all of their children. So G = (people, family) is a hypergraph. Contrast this with the binary relation "married to," which connects a man and a woman, or "child of," which is directed from a child to his or her father or mother.

Author: PEB

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Entry modified 26 August 2014.
HTML page formatted Mon Feb 2 13:10:39 2015.

Cite this as:
Paul E. Black, "hypergraph", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 26 August 2014. (accessed TODAY) Available from: