Suppose that a flow network G = (V, E) violates the assumption that the network contains a path s t for all

Suppose that a flow network G = (V, E) violates the assumption that the network contains a path s ⤳ ν ⤳ t for all vertices ν ∈ V. Let u be a vertex for which there is no path s ⤳ u ⤳ t. Show that there must exist a maximum flow f in G such that f (u, ν) = f (ν, u) = 0 for all vertices ν ∈ V.