(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 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 Wed Mar 13 12:42:46 2019.

Cite this as:

Paul E. Black, "hypergraph", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 26 August 2014. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/hypergraph.html