I am modeling a traffic network with a simple edge-weighted graph. The edge weights represent the capacity of each road. I would like to measure the maximum flow the network can accept.
In order to implement any kind of max-flow algorithm, I know part of the trick is changing each undirected weighted edge into a pair of directed edges with identical weights.
My problem is I do not have a specified source or sink for my network. The only thing I can think of is to try every possible pairing of distinct vertices as a source/sink pair, but that leaves me $10^{10}$ pairings to check, which is untenable.
Any other ideas on how to approach this?