Hyperedge in the context of Hypergraph

In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.

Formally, a directed hypergraph is a pair ${\displaystyle (X,E)}$, where ${\displaystyle X}$ is a set of elements called nodes, vertices, points, or elements and ${\displaystyle E}$ is a set of pairs of subsets of ${\displaystyle X}$. Each of these pairs ${\displaystyle (D,C)\in E}$ is called an edge or hyperedge; the vertex subset ${\displaystyle D}$ is known as its tail or domain, and ${\displaystyle C}$ as its head or codomain.