I've was studying about network flows and I encountered the special case where vertices also have a capacity. This problem problem can be converted to the conventional one without vertex capacities. This process is for example described here:https://en.wikipedia.org/wiki/Maximum_flow_problem#Maximum_flow_problem_with_vertex_capacitiesThe problem is that I'm not really understanding why this maintains the property  flow conversation of the flow function. Could someone explain it to me? In general, could someone explain to me why is the converted flow network without vertex capacities a valid flow network? Why was the the original flow network with vertex capacities a valid flow network?I understood that this maintains the property capacity constraint, since we do not modify the flow values of the edges, assuming that the original flow network with vertex capacities and its flow function are well-formed.
How can a network flow with vertex capacities be equivalent to one without them?
graphs;graph theory;network flow