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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?

  1. Only $P_1$
  2. Only $P_2$
  3. Both $P_1$ and $P_2$
  4. Neither $P_1$ nor $P_2$
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