Transport on weighted Networks: when correlations are independent of degree

TL;DR

This paper investigates weight-weight correlations in weighted networks independent of node degree, introduces a method to generate such correlations, and examines their impact on network transport efficiency, supported by real-world examples.

Contribution

It presents a simple method to incorporate weight correlations in uncorrelated networks and analyzes their effects on transport properties, extending understanding beyond degree-dependent correlations.

Findings

Positive weight correlations enhance transport efficiency.

Weight correlations are present in real-world social and transport networks.

The proposed method enables controlled study of weight correlation effects.

Abstract

Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.