Hypergraph isomorphism ($\varphi :V(H)\stackrel{\sim }{\to }V(K)$)

A hypergraph isomorphism is a bijection of the vertex sets such that a subset is a hyperedge of the first hypergraph if and only if its image is a hyperedge of the second. The condition preserves both edges and nonedges. In the two-uniform case it is the usual relation of isomorphic graphs.