I was looking for a cut of the following graph of a problem of maximum flow. Here are its capacities :
As far as the only nodes that have saturated edges are the upper external ones, it would be :
It seems to be strange to be only the top nodes, isn't it ? Yet the more strange is when we apply the max-flow min-cut theorem :
the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in the minimum cut, i.e. the smallest total weight of the edges which if removed would disconnect the source from the sink.
Yet, if I sum up all top edges I get $17$, whereas the maximum amount of flow passing from the source to the sink is $18$.