I was playing around with https://visualgo.net/en/maxflow when I realized a pattern:
Take this graph, for example. We notice that the min-cut divides the graph into two sets of nodes: {0, 2, 3, 6} and {1, 4, 5, 7}.
I noticed that choosing any node within {0, 2, 3, 6} as a source and {1, 4, 5, 7} as a sink, or vice versa, produces the same min-cut edges.
Is this true in general? As in, will the min-cut produced be the same for any source-sink pair from one-side of a min cut to the other?