Vertex of a hypergraph ($v\in V(H)$)

A vertex of a hypergraph $H=(V,E)$ is an element of its ground set $V$. Each hypergraph edge is a subset of $V$, and isolated vertices may belong to no edge. In a multipartite hypergraph, each vertex additionally lies in exactly one of the specified parts. This is the hypergraph analogue of a vertex of a graph, allowing edges of cardinality other than two.