The study of maximum flow in a network is closely tied up with the concept of a cut, which is a set A of arcs such that each path from v to w includes an arc in A. thus, a cut in a network is a vw- disconnecting set in the corresponding digraph D. The capacity of a cut is the sum of the capacities of the arcs in the cut. We are concerned mainly with those cuts whose capacity is as small as possible, the so-called minimum cuts. In Fig 29.3, a minimum cut consists of the arcs vz, xz, yz and xw, but not the arc zx; the capacity of this cut is 2+2+2=6.