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==Symmetric hypergraphs==

==Symmetric hypergraphs==

The ''{{visible anchor|rank}}'' <math>r(H)</math> of a hypergraph <math>H</math> is the maximum cardinality of any of the edges in the hypergraph.  If all edges have the same cardinality ''k'', the hypergraph is said to be ''uniform'' or ''k-uniform'', or is called a ''k-hypergraph''.  A graph is just a 2-uniform hypergraph.

The<math>r(H)</math> of a hypergraph <math>H</math> is the maximum cardinality of any of the edges in the hypergraph.  If all edges have the same cardinality ''k'', the hypergraph is said to be ''uniform'' or ''k-uniform'', or is called a ''k-hypergraph''.  A graph is just a 2-uniform hypergraph.

The degree ''d(v)'' of a vertex ''v'' is the number of edges that contain it. ''H'' is ''k-regular'' if every vertex has degree ''k''.

The degree ''d(v)'' of a vertex ''v'' is the number of edges that contain it. ''H'' is ''k-regular'' if every vertex has degree ''k''.