  This paper examines the Balanced Submodular Flow Problem, that is the problem
of finding a feasible submodular flow minimizing the difference between the
flow values along the edges. A min-max formula is given to the problem and an
algorithm is presented to solve it using $O(m^2)$ submodular function
minimizations. Then, these result are extended to the weighted version of the
problem. Finally, the Balanced Integer Submodular Flow Problem is discussed.
