(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 relations "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

Go to the Dictionary of Algorithms and Data Structures home page.

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Entry modified 18 October 2007.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "hypergraph", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 18 October 2007. (accessed TODAY) Available from:

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