Let's look at a different problem with some similar structure.
We've still got a source, nodes, and water flowing around. But now we want to just make sure that everyone (all nodes) get some water (or electricty or ...).
For each pair of cities (u,v) that have a pipe between them, there is a cost w(u,v) for keeping the pipe open.
Choose a set of pipes to keep open such that:
Answer?
