Quick questions on Flow Networks - TCE Mathematics Applications (Tasmania)

A cut divides the network into two groups of vertices, one containing the source and the other containing the sink, by cutting through some edges. The capacity of the cut is the total capacity of the edges that go from the source side to the sink side.

The single skill examiners test most is counting a cut's capacity. Draw a line that separates the source side from the sink side, then add only the capacities of edges that cross from the source side to the sink side. Edges that run back the other way, from the sink side to the source side, contribute nothing to that cut. A cut may slice through edges anywhere in the network, not just those at the source or sink, so be systematic about which side each endpoint lies on before deciding whether an edge counts.

Once you know the minimum cut, you also know how to increase the maximum flow: enlarge a bottleneck edge that lies on the minimum cut. Upgrading an edge that is not on the minimum cut achieves nothing, because the bottleneck is elsewhere. This is why TASC questions that ask which pipes to upgrade are really asking you to name the edges crossed by the minimum cut.