Let G=(V,A) be a graph with vertex set V and arc set a. A flow for G is an arbitrary real-valued function defined on the arcs A. A flow f is called max-balanced if for every cut W,ΘℝWℝV, the maximum flow over arcs leaving W equals the maximum flow over arcs entering W. The authors describe ten characterizations of max-balanced flows using properties of graph contractions, maximum cycle means, flow maxima, level sets of flows, cycle covers, and minimality with respect to order structure in the set of flows derived from a given flow by reweighting. They also give a linear programming based proof for an existence result of Schneider and Schneider.
