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Network flows are used to model concepts like traffic or water pipe systems. The basic idea is to move as many units of flow from source to sink nodes via edges with limited capacity.

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How to find a minimum cut of a network flow?

The minimum cut is a partition of the nodes into two groups. Once you find the max flow, the minimum cut can be found by creating the residual graph, and when traversing this residual network from th …
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How to find the subsets S and T and the min-cut of this graph?

As settled in the Question's comments: The residual graph, as presented, is incomplete. The residual graph must include the non-zero reverse flow arcs. Then anything reachable from the source $S$ in t …
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