Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a real-valued function $f:V\times V\to R$:
$P_1$: For all $u,v\in V,\ f(u,v)=-f(v,u)$
$P_2$: $\sum_{v\in V} f(u,v)=0$ for all $u\in V$
Which one of the following is/are correct?
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