The definition that I know for dual graph is for a undirected graph.
I wonder if dual graph can be defined for a directed graph? If yes, how is the orientation of the dual graph determined?
The motivation of my question is that in planar undirected s-t network, the minimum s-t cut problem in the network and the shortest s-t path problem in its "dual" network can be converted from each other. Please refer to my earlier question. I then wonder what about the network is directed?