We address the problem of assigning optimal routes in a graph that transports two given densities across its nodes. The traffic flow along each edge at a given time induces a metric on the graph, with respect to which the routes must be geodesics. The resulting configurations are known as Wardrop equilibria. Additionally, a central planner may require the assignment to be efficient - that is, to minimize the Kantorovich functional associated with this metric. Under symmetry assumptions on the cost functions, the problem reduces to a class of variational problems with divergence constraints, originally studied by Beckmann. The corresponding partial differential equations are highly degenerate and belong to a fascinating class of problems that remains rich with open questions and opportunities for further exploration. Part of this work is a collaboration with Sergio Zapeta Tzul, former master's student at CIMAT and current PhD student at the University of Minnesota.