Characterization and Modeling of weighted networks

TL;DR

This paper reviews tools for analyzing weighted networks, presents case studies on airline and collaboration networks, and discusses a model explaining observed weight-topology correlations in complex systems.

Contribution

It introduces a model for weighted network formation based on the dynamic coupling of topology and weights, explaining empirical features.

Findings

Broad distributions of network quantities

Existence of weight-topology correlations

Weights significantly influence network structure

Abstract

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical infrastructures and social systems, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of weights when new links are introduced in the system.