# graph theory – Potential flow and impact vectors

Let $$f$$ to be a function on the arc game $$A$$ of an acyclic network $$N (x, y)$$ (right here $$x$$ is the source and $$y$$ l & # 39; sink). assume $$0 leq f (a) leq c (a)$$ for everyone $$a in A$$ ($$c$$ is the capacity function). CA watch $$f$$ is a flow if and only if it is a non-negative linear combination of vectors of incidence of $$(x, y)$$paths.