Weighted Configuration Model

TL;DR

This paper investigates the behavior of the configuration model for uncorrelated random networks with power-law degree sequences below an exponent of two, revealing weighted network characteristics and correlations.

Contribution

It provides new insights into the weighted network structure and correlations when the degree sequence follows a power law with exponent less than two.

Findings

Network behaves as a weighted network with non-trivial correlations.

Numerical simulations confirm the theoretical analysis.

Results extend understanding of configuration models in heavy-tailed degree distributions.

Abstract

The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the resulting network can be viewed as a weighted network with non trivial correlations between strength and degree. Our results are tested against large scale numerical simulations, finding excellent agreement.