Question: I need to find the minimum cut on a graph. I've been reading about flow networks, but all I can find are maximum flow algorithms such as Ford-Fulkerson, push-relabel, etc. Given the max flow-min cut theorem, is it possible to use one of those algorithms to find the minimum cut on a graph using a maximum flow algorithm? How?

The best information I have found so far is that if I find "saturated" edges i.e. edges where flow equals capacity, those edges correspond to the minimum cut. Is that true? It doesn't sound 100% right to me. It is true that all edges on the minimum cut will be saturated, but I believe there might also be saturated edges which are out of the minimum cut "path".

Answer: 
So, to give the exact procedure how to obtain the minimum cut:

1. Run Ford-Fulkerson algorithm to find the max flow and to get the residual graph1.
2. Run BFS **on the residual graph** to find the set of vertices that are reachable from source in the residual graph (respecting that you can't use edges with 0 capacity in the residual graph).
IMPORTANT: You have to use reverse edges in the residual graph to find the correct set of reachable vertices!!! [(See this algorithm)](http://www.geeksforgeeks.org/minimum-cut-in-a-directed-graph/ "algorithm")
3. All edges **in the original graph** which are from a reachable vertex to non-reachable vertex are minimum cut edges. Print all such edges.

1 Graph in which the capacity of an edge is defined like it's original capacity minus its flow (flow from the maximum flow network).
One way to understand is, let's define a cut as two sets S and T, which will include s and t, respectively.

Now, add all vertices in S that are reachable from s in the residual network and put the remaining edges in T. This will be one cut.

Second, cut can be formed by putting all vertices in T that are reachable from t in the residual network and put the remaining vertices in S.

Take a look at this video to find out how do we find the vertices reachable from s and t.

<https://www.youtube.com/watch?v=FIJaXfUIXJA&index=4&list=PLe-ggMe31CTduQ68XQ-sVj32wYJIspTma>