# Definition of capacity of cut in a flow network

In the flow network below, an S-T cut is made.

The net flow across the cut is $12-4+11=19$.

The capacity of the cut is $12+14=26$. The "backwards" edge $(v_3,v_2)$ is not counted when calculating capacity.

Why isn't the capacity of a cut defined to be $(\text{capacity of forward edges}) - (\text{capacity of backwards edges})$? This is more intuitive.