Modeling the evolution of weighted networks

TL;DR

This paper introduces a comprehensive model for the growth of weighted networks, capturing their dynamic evolution and hierarchical structure, aligning with properties observed in real-world systems.

Contribution

It proposes a novel coupled growth and weight evolution model that reproduces key statistical features of real weighted networks, including scale-free behavior and hierarchical architecture.

Findings

The model produces scale-free degree distributions with tunable exponents.

Generated networks exhibit clustering and connectivity correlations.

The approach can incorporate additional randomness and non-linear effects.

Abstract

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree.