Scaling of internode distances in weighted complex networks

Abstract

We extend the previously observed scaling equation connecting the internode distances and nodes' degrees onto the case of weighted networks. We show that the scaling takes a similar form in the empirical data obtained from networks characterized by different relations between node's strength and its degree. In the case of explicit equation for s(k) (e.g. linear or scale-free), the new coefficients of scaling equation can be easily obtained. We support our analysis with numerical simulations for Erdos-Renyi random graphs with different weight distributions.