Empty hypergraph: it is a hypergraph with no edges. , Non-simple (or multiple) hypergraph allows to have loops or repated edges which means there can be two edges contains same set of vertices. Simple hypergraph: which contains no loops and no repeated edges. k {\displaystyle k} -uniform hypergraph. it is a hypergraph where each edge contains precisely k {\displaystyle k} vertices. d {\displaystyle d} -regular hypergraph: is a hypergraph where every vertex has degree d {\displaystyle d} . Acyclic hypergraph. it is a hypergraph which does not contain any cycles.