Formally, a hypergraph H {\displaystyle H} is a pair H = ( X , E ) {\displaystyle H=(X,E)} where X {\displaystyle X} is a set of elements called nodes or vertices, and E {\displaystyle E} is a set of non-empty subsets of X {\displaystyle X} called hyperedges or edges. Therefore, E {\displaystyle E} is a subset of P ( X ) ∖ { ∅ } {\displaystyle {\mathcal {P}}(X)\setminus \{\emptyset \}} , where P ( X ) {\displaystyle {\mathcal {P}}(X)} is the power set of X {\displaystyle X} . The size of vertex set is called the order of the hypergraph, and the size of edges set is the size of the hypergraph.