The apparently naive representation of a complex system as a collection of binary relations between indistinguishable units has since long proved to be a powerful tool for understanding dynamical systems. An important feature of interconnected systems is their ability to exchange information efficiently [1]. Assuming that the efficiency of a communication decreases as the distance between sender and receiver increases, one can easily quantify the communication efficiency of a networked system by the harmonic average of shortest-path distances. While in the topological case this descriptor is normalised in [0,1] by definition, in the weighted case it needs to divided by the efficiency of an ideal network. In this work [2] we define a physically-grounded procedure to build the idealised version of a given network G, whose edge weights encode the intensities of the interactions. This procedure can be seen as adding to G shortcuts between connected but non-adjacent nodes, delivering the total flow (sum of weights) along their weighted shortest (or least resistance) path. The applications to real networks show that reducing the weight heterogeneity (by removing heavy links or re-distributing large flows) may lead to a more efficient communication.
