As stated in this paper, there is a technique to reformulate a multi-commodity flow problem (MCF) with undirected edges to its equivalent version with directed edges.
By quoting them:
The reformulation involves adding two additional nodes and four additional arcs for each undirected arc.
However, just from this sentence I can't figure out the shape of the new graph. I also have problem to retrieve the original reference describing in detail such transformation.
Can someone explain how to do this? Also, considering that I am working with a minimisation MCF, is there a more efficient transformation?