Scaling of internode distances in weighted complex networks

TL;DR

This paper generalizes the scaling relationship between internode distances and node degrees to weighted networks, supported by empirical data and simulations, providing a framework for understanding weighted complex network structures.

Contribution

It extends the scaling equation to weighted networks and derives new coefficients for different strength-degree relations, enhancing network analysis methods.

Findings

Scaling equation applies to weighted networks with various strength-degree relations

Explicit formulas for s(k) enable easy calculation of scaling coefficients

Numerical simulations validate the extended scaling law

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.