What's an intuitive explanation of the max-flow min-cut theorem? I'm about to read the proof of the max-flow min-cut theorem that helps solve the maximum network flow problem. Could someone please suggest an intuitive way to understand the theorem?

Imagine a complex pipeline with a common source and common sink. You start to pump the water up, but you can't exceed some maximum flow. Why is that? Because there is some kind of bottleneck, i.e. a subset of pipes that transfer the fluid at their maximum capacity--you can't push more through. This bottleneck will be precisely the minimum cut, i.e. the set of edges that block the flow. Please note, that there may be more that one minimum cut. If you find one, the you know the maximum flow; knowing the maximum flow you know the capacity of the cut.
Hope that explains something ;-)
