The digraph $ G = (V, E)$ is called cyclic if $\exists k ≥ 1$ circuits in $ G, C_1, . . . , C_k,$ whose set of vertices, $V (C_1), . . . , V (C_k),$ forms a partition of $V (G)$. Prove that you can test in polinomial time (in relation to $|V | + |E|$) if the digraph $ G = (V, E)$ is cyclic by solving the maximum flow problem in a network of flows conveniently constructed.
I know this problem is not strictly mathematical but I will be grateful for any pointers or indications.