Correlations in weighted networks

TL;DR

This paper develops a statistical framework to analyze correlations in weighted networks, introduces null models, and demonstrates the significance of weights in understanding real-world complex systems.

Contribution

It provides new metrics for weighted network correlations, proves uncorrelated weighted networks are impossible, and offers an algorithm for generating null models.

Findings

Correlations are intrinsic to weighted networks due to structural constraints.

The introduced metrics effectively quantify correlations in real networks.

Null models help in understanding the role of weights in network structure.

Abstract

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary $P(k,s)$ to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.