While graph edges are 2-element subsets of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting k nodes.)