Supplementary Materials

We recall here the entropy-like measure {S F } proposed in [1] and we compare it to our network entropy measure S. The results presented in [1] are substantially different from our achievements and the reason lies in the conceptual foundation of the two measures. We clarify their relation thank to a simple toy model. The “entropy of information flux distribution" {S F } is a single-node entropy measure, i.e. {S F } is a collection of entropy values, one for each node of the designed network (i = 1, ...N where N is the total number of nodes). This measure behaves similarly to the local disparity-heterogeneity index (or participation ratio PR) of weighted networks, and is defined as follows: