Weighted scale-free network with self-organizing link weight dynamics

TL;DR

This paper introduces a model for weighted scale-free networks where link weights depend on node strengths through a tunable parameter, leading to self-organizing dynamics that replicate real-world network features.

Contribution

The study presents a novel model with a non-linear weight definition and self-organizing dynamics, producing tunable exponents in scale-free networks.

Findings

Exponents of weighted networks are tunable with parameter α.

The model reproduces key features of real-world weighted networks.

Weight distribution is conjectured to be similar across scale-free networks.

Abstract

All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $\alpha$ as $w_{ij}=(s_is_j)^\alpha$, $s_i$ and $s_j$ are the strengths of two end nodes of the link and $\alpha$ is a continuously tunable positive parameter. In addition the definition of strength as $s_i= \Sigma_j w_{ij}$ results a self-organizing link weight dynamics leading to a self-consistent distribution of strengths and weights on the network. Using the Barab\'asi-Albert growth dynamics all exponents of the weighted networks which are continuously tunable with $\alpha$ are obtained. It is conjectured that the weight distribution should be similar in any scale-free network.