Circulation in a flow network
= Circulation in a flow network
{title2=$\sum_jf_{ij}=\sum_jf_{ji}\text{ at every }i$}
= Network circulation
{synonym}
A <network circulation> is a <flow> with zero net supply at every vertex. A feasible residual <network circulation> changes one feasible flow into another with the same prescribed supplies. It decomposes into directed cycles, giving the negative-cycle optimality test for <minimum-cost flow>.