Circuit rank
![This graph has circuit rank r = 2 because it can be made into a tree by removing two edges, for instance the edges 1–2 and 2–3, but removing any one edge leaves a cycle in the graph.](/Images/godic/202501/04/6n-graf.svg0602.png")
In graph theory, a branch of mathematics, the circuit rank of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making it into a tree or forest. Alternatively, it can be interpreted as the number of independent cycles in the graph. Unlike the corresponding feedback arc set problem for directed graphs, the circuit rank r is easily computed using the formula