Let $G=(X,U)$ be a connected digraph and $(G,c)$ a network. Let $s$ and $t$ be different vertices such that $d^+(s)>0$ and $d^-(t)> 0 $. Show that if there is no path from $s$ to $t$ in $G$ then the null flow is a maximum flow from $s$ to $t$ in the $(G,c)$ network.
I was thinking of doing it by contradiction, supposing that the maximal flow is not null for this network, so we would have to have a path from $s$ to $t$ which contradicts the hypothesis. I'm not sure, it's just an idea. Does someone have any hint on how can I start the proof?
Yes, you are essentially proving the contrapositive, which is a reasonable approach.