# Flow Network - ## Definition - _capacity function_: $c(u, v) \ge 0$ - _source_ $s$ and _sink_ $t$, so that $\exists s \leadsto v \leadsto t$ $\forall v \in V$. - _flow_: $f: V \times V \to \mathbb R$ - $0 \le f(u, v) \le c(u, v)$ - $\displaystyle\sum_{v\in V} f(v, u) = \sum_{v\in V}f(u, v)\; \forall u \in V - \{s, t\}$ - $f(u, v) = 0\; \forall (u, v) \notin E$ - _supersource_ and _supersink_