Editing Cyclomatic number (section)

==Matroid rank and construction of a minimum feedback edge set==
The cyclomatic number of a graph {{mvar|G}} may be described using [[matroid theory]] as the [[matroid rank|corank]] of the [[graphic matroid]] of {{mvar|G}}.<ref>{{citation|title=Graphs and Hypergraphs|volume=6|series=North-Holland Mathematical Library|first=Claude|last=Berge|authorlink=Claude Berge|publisher=Elsevier|year=1976|isbn=9780720424539|page=477|url=https://books.google.com/books?id=Wy2mhanRnk4C&pg=PA477}}.</ref> Using the greedy property of matroids, this means that one can find a minimum set of edges that breaks all cycles using a [[greedy algorithm]] that at each step chooses an edge that belongs to at least one cycle of the remaining graph.

Alternatively, a minimum set of edges that breaks all cycles can be found by constructing a [[spanning forest]] of {{mvar|G}} and choosing the [[Complement (set theory)|complementary]] set of edges that do not belong to the spanning forest.