Circuit rank

Definition

Definition for a finite graph

Suppose $G$ is a finite undirected graph. The circuit rank of $G$, also called the cyclotomic number of $G$, is defined in the following equivalent ways:

1. It is the minimum number of edges that needs to be removed from the edge set of $G$ to make it a forest (i.e., an acyclic graph)
2. It is given by $|E(G)|-|V(G)|+c$ where $V(G)$ is the vertex set, $E(G)$ is the edge set, and $c$ is the number of conncted components of $G$.