Statistical analysis of weighted networks

TL;DR

This paper evaluates various statistical measures for weighted networks, comparing their definitions and analyzing how they depend on connection weights, revealing new regularities useful for network characterization.

Contribution

It introduces the relative perturbation norm as a new index for assessing weight distribution and clarifies the significance of different weighted clustering coefficient definitions.

Findings

Identified differences between definitions of weighted clustering coefficient.

Introduced the relative perturbation norm for weight distribution analysis.

Discovered new statistical regularities in weighted networks.

Abstract

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.