We will address the problem of assigning optimal routes in a graph that transport two given densities over the nodes. The occupation of each edge at a given time defines a metric over this graph, for which the routes must be geodesics. This model may describe for example the congestion of a city and its solutions are known as Wardrop equilibria. Additionally, a central planner can require that the assignment is efficient, meaning it minimizes the Kantorovich functional arising from this metric. In this presentation, we will characterize this problem in terms of a partial differential equation and illustrate a simple case. This work is a collaboration with Sergio Zapeta Tzul, a former MSc student at CIMAT and current PhD student at the University of Minnesota.