I was going through the Ford-Fulkerson(FF) algorithm. The given graph is directed and there is an edge from A to B with capacity y. Now sending a flow of x units (x < y) from A to B is equivalent to sending -x units from B to A, so we add a back edge from B to A of capacity x units. And the FF algorithm can send a flow of x units from B to A in the future. But the property of a directed graph is that you can go from A to B and not from B to A. As an analogy let me take the traffic network and say the path from A to B is one-way. Adding a back edge and sending a flow via that back edge contradicts with our assumption that the path from A to B is one-way. Am I missing something? Or there is a better intuitive way to understand this?