Universal scaling of distances in complex networks

TL;DR

This paper uncovers a universal logarithmic scaling law for distances between nodes in various complex networks, linking mean distances to node degrees and network clustering.

Contribution

It introduces a simple theoretical model explaining the universal distance scaling observed across diverse network types.

Findings

Distances scale as A - B log(k_i k_j) across networks

Parameters depend on average neighbor degree and clustering

Scaling holds over several orders of magnitude

Abstract

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to <l_{ij}>=A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree <k>_nn calculated for the nearest neighbors and on network clustering coefficients.