Let \(G(V,E,\gamma)\) be an biconnected graph and let \(C(V_c,E_c)\) be a cycle in \(G\)^{1}.
\(C\) is called separating if there are at least two pieces of \(G\) with respect to \(C\) . \(C\) is called non-separating if there only one piece of \(G\) with respect to \(C\) .
In the following graph, the cycle (blue) is non-separating, since it has only one piece \(P\) (highlighted orange on the right).
Another cycle in the same graph (also marked blue) is separating, since it has \(6\) pieces \(P_1,P_2,\ldots,P_6\) (highlighted orange on the right):
Please note that in a biconnected graph such a cycle always exists. ↩