Here’s a demonstration of Max Cut Min Flow.  The demo only considers capacities which go in one direction between two vertices.

 

http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/maxflow/MaxflowApp.shtml?demo5

 

Here’s an explanation of the algorithm.

 

Ford-Fulkerson algorithm - Wikipedia, the free encyclopedia

 

Max-flow min-cut theorem - Wikipedia, the free encyclopedia