NIST

hypergraph

(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.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

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: http://www.nist.gov/dads/HTML/hypergraph.html

to NIST home page