I am going through the book "Network Flows" by Ahuja et al. In chapter 19.2 "MAXIMUM WEIGHT CLOSURE OF A GRAPH", I find this example of turning a vertex-weighted (positive or negative) digraph into a flow network. The min-cut in the flow network is supposed to correspond to a max-weight closure in the original graph.
Here, the max weight closure is supposed to be
3, 4, 5 and the capacity of the corresponding cut in the flow network is (8+10). However, the min cut in the flow network is actually just
s, with capacity (8+7), which does not correspond to any closure in the original graph. What am I missing?