---
tag: CH2JRZNX7V
kind: concept
name: Hypergraph
msc: [05C65]
sources:
  - url: https://en.wikipedia.org/wiki/Hypergraph
same_as:
  wikidata: Q840247
  wikipedia: Hypergraph
---

## Summary

A hypergraph is a generalisation of a [[graph|00C0BR7D7H]] in which an edge may join any number of vertices.
Formally it is a set of vertices together with a family of subsets of it, the hyperedges.
Hypergraphs are the natural language for set systems, [[block designs|4JCSS2Z1BA]] and many problems of extremal combinatorics.
The node [[hypergraph|2KM46K20DZ]] gives the precise definition.

## Explanations

### L1 human

In a graph, an edge links two people, like a friendship.
In a hypergraph, an edge can be a whole club with any number of members.
For example, the students of a school are the vertices and each class is a hyperedge.
When every hyperedge has exactly two members, a hypergraph is just a graph.