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When dealing with Minimum Cuts, what do you do when you are given an undirected graph without edge weights and no source and sink node? How do you modify the graph so that it can be used with Ford-Fulkerson?

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  • $\begingroup$ Does your graph have supply/demand information? What are you trying to work out? $\endgroup$ – Alex J Best Apr 7 '14 at 22:47
  • $\begingroup$ Nope, all I'm given is G=(V,E), a typical undirected graph and I'm trying to find the Minimum Cut. I just can't figure out how to reduce it to the Max-Flow problem $\endgroup$ – Alex Chumbley Apr 7 '14 at 23:46
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Replace each edge by two edges, one for each direction. Fix a vertex $t\in V$, any vertex. Now simply do Max-$s$-$t$-Flow for each $s\in V\setminus\{ t\}$ and record the smallest $s$-$t$-cut every time. When you have tried them all, choose the smallest.

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