Hyperedge ($E\in \mathcal{E}(H)$)

A hyperedge is a member of the edge family of a hypergraph. In an $r$-uniform hypergraph it is an $r$-element subset of the vertex set. For $r=2$ it is an ordinary edge of a graph. A simple hypergraph has no repeated hyperedges; a multihypergraph records multiplicities.