hyperedges

A hyperedge is a generalization of the concept of an edge in graph theory. In a standard graph, an edge connects exactly two vertices. A hyperedge, also known as a compound edge or a set-valued edge, can connect any number of vertices. This means a hyperedge can link two vertices, three vertices, or even more vertices simultaneously.

Hypergraphs are mathematical structures that use hyperedges. A hypergraph consists of a set of vertices and a set of hyperedges, where each hyperedge is a subset of the vertices. This allows for the modeling of relationships that are not simply pairwise. For instance, in a social network, a hyperedge could represent a group meeting, involving multiple individuals. In computer science, hypergraphs are used in areas like database design and network analysis.

The definition of a hyperedge allows for greater flexibility in representing complex relationships. While traditional edges represent binary connections, hyperedges can capture n-ary relationships where n is greater than or equal to two. The study of hypergraphs and hyperedges provides a powerful tool for analyzing structures with multifaceted connections.