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Let Fₔ, ₕ be the maximal flow from u to v in a network N = (V, E, c). We construct the matrix (\ Fₔ, ₕ, Fₕ, ₔ \ |u, v V) by solving |V| 2|V| individual max-flow problems for N. There is a tree network N = (V, E, c) that stores minimal cuts corresponding to min \ Fₔ, ₕ, Fₕ, ₔ \ for all u, v. N can be constructed by solving |V| 2|V| individual max flow problems for the given network which can be done within O (|V|⁴) steps using the Dinic–Karzanov algorithm. We design an algorithm that computes the edge connectivity k of a directed graph within O (k |E| |V|) steps.
C. P. Schnorr (Tue,) studied this question.