 Network dual potential

A vertex potential in the dual of an uncapacitated minimum-cost flow yields the edge inequalities ${\pi }_i-{\pi }_j\le c_{ij}$. Its objective is ${\sum }_i{\pi }_i{b}_i$. Adding a common constant leaves all network reduced costs and the objective unchanged when total net supply is zero. Potentials tight on a spanning tree are fixed up to this common constant.