In a directed graph G, we define the arc connectivity, ali, j), of an ordered pair [i, j) of nodes as the minimum number of arcs whose deletion from the network eliminates all the directed path from node ito nodej. We define the arc connectivity of a network Gas a(G) = min{a[i,j):[i,j) EN x N}. Describe an algorithm for determining a(G) in O(min{n513m, m 2}) time and prove that this algorithm correctly determines the arc connectivity of any directed network. (Hint: Let p be a node in G of minimum degree. Determine a[p,j] and a[j, p) for allj, and take the minimum of these numbers.)