Consider a variant of max-flow networks in which all vertices different from the source and the sink have a maximum capacity. As we know, Such a network can be transformed into a usual max-flow network such that every maximum flow provides a solution to the original problem.
My question is
How to do such a transformation?
Thank you.
The trick would be to separate a vertex $v$ into two new vertices $v^-$ and a $v^+$ in. In a directed graph you then connect all incoming edges to $v$, denoted $\delta^-(v)$, to $v^-$ and all outgoing edges, denoted $\delta^+(v)$ to $v^+$. Finally, you add an edge from $v^-$ to $v^+$ with capacity equal to the capacity the vertex $v$ originally had. This way you have turned the vertex capacity to an edge capcity and thus you can use the normal max flow solution methods.