I am very new to integer linear programming and trying to solve a
classical problem at the moment, yet I couldn't find anything similar
on the web really. I am working with AMPL (or actually ZIMPL, a subset).

I want to calculate the minimum cut of a simple network, by actually
enumerating all possible cuts and not by calculating the maximum
flows. The idea is to divide a network with, say, one source, two
relay nodes connected with every other node and two sinks, in all
possible cuts where the sinks and the source are not in the same part
(which should result in four possibilities, if i counted correctly).
Then the connections going over the cut shall be counted (all having the
same capacity for the sake of simplicity).

The max flow formulation was easy, but I really am having problems
with this one. Any help or directions where to read more about
implementing this, would be highly appreciated.

Thanks very much!