Editing Cyclomatic number (section)

== For hypergraphs ==
The cyclomatic number of a [[hypergraph]] can be derived by its [[Levi graph]], with the same cyclomatic number but reduced to a simple graph. It is
<math display=block>r = g - (v + e) + c,</math>
where {{mvar|g}} is the [[Handshaking lemma|degree sum]] (and the number of edges in the Levi graph), {{mvar|e}} is the number of hyperedges in the given hypergraph, {{mvar|v}} is the number of [[vertex (graph theory)|vertices]], and {{mvar|c}} is the number of [[component (graph theory)|connected components]].

The ''degree sum'' of a hypergraph is the sum of the degrees of all the vertices, reducing to {{math|2''e''}} for a simple graph, or {{math|''ke''}} for a {{mvar|k}}-uniform hypergraph. This formula is symmetric between vertices and edges which demonstrates a hypergraph and its dual hypergraph have the same cyclomatic number.