cycle rank | cyclomatic number | graph Betti number | graph nullity

The circuit rank μ, is the smallest number of graph edges which must be removed from an undirected graph on m graph edges and n nodes such that no graph cycle remains. The circuit rank also gives the number of fundamental cycles in a cycle basis of a graph (Harary 1994, pp. 37-40; White 2001, p. 56). The concept was first introduced by Gustav Kirchhoff, and has been referred to by a number of different names and symbols as summarized in the following tables.

Balaban index | Betti number | cactus graph | connected component | edge count | graph cycle | vertex count