Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a real-valued function $f:V \times V \rightarrow R$:
$P_1$: For all $u, v, \in V, \: f(u,v)=-f(v,u)$
$P_2$: $\underset{v \in V}{\Sigma} f(u,v)=0$ for all $u \in V$
Which one of the following is/are correct?
- Only $P_1$
- Only $P_2$
- Both $P_1$ and $P_2$
- Neither $P_1$ nor $P_2$