# Is skew symmetry required for a flow network?

From Wikipedia:

$G(V,E)$ is a finite directed graph in which every edge $\ (u,v) \in E$ has a non-negative, real-valued capacity $\ c(u,v)$. A flow network is a real function $\ f:V \times V \rightarrow \mathbb{R}$ with the following three properties for all nodes $\ u$ and $\ v$:

Capacity constraints: ...

Skew symmetry: $\ f(u,v) = - f(v,u)$. The net flow from $\ u$ to $\ v$ must be the opposite of the net flow from $\ v$ to $\ u$.

Flow conservation:...

For any two vertices $v$ and $u$, the two edges $(v,u)$ and $(u,v)$ may not both exist.

Even if they both exist, I don't understand why skew symmetry may be required.

Also I didn't see "Skew symmetry" is required in the definition in books such as Introduction to graph theory by West, and Combinatorial optimization by Korte and Vygen).

So I wonder if skew symmetry is or may be required for a flow network?

Thanks!

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Usually, one represents flow like this in a matrix, where entry at position $(u,v)$ is the flow from $u$ to $v.$ If there is no such edge, then we consider the flow to be 0.