(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, ...} ∈ 2^{V}}. (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