Flow balance
= Flow balance
{title2=$\sum_j f_{ij}-\sum_jf_{ji}=b_i$}
A flow balance prescribes net outgoing minus incoming flow at a vertex. Positive $b_i$ is supply and negative $b_i$ is demand; zero is ordinary <flow conservation>. Summing all balances requires total supply to equal total demand. In a <directed graph>, these equations are represented by the <oriented incidence matrix>.