Let $F_{u,v} $ be the maximal flow from u to v in a network $\mathcal{N} = (V,E,c)$. We construct the matrix ($\min \{ F_{u,v} ,F_{v,u} \} |u,v \in V$) by solving $|V|\log 2|V|$ individual max-flow problems for $\mathcal{N}$. There is a tree network $\mathcal{N} = (V,\bar E,\bar c)$ that stores minimal cuts corresponding to min $\{ F_{u,v,} F_{v,u} \} $ for all $u,v$. $\bar{\mathcal{N}}$ can be constructed by solving $|V|\log 2|V|$ 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 $O(k\cdot |E|\cdot |V|)$ steps.