The Structure and Growth of Weighted Networks

TL;DR

This paper introduces a theoretical model for weighted network evolution, extending the Barabasi-Albert model with geometric Brownian motion for link weights, validated by simulations and trade data.

Contribution

It presents a novel framework combining network growth with stochastic weight evolution, aligning well with real-world weighted network features.

Findings

Accurately predicts link growth and intensity

Replicates size-variance relationships of link weights

Captures scale-free network structure

Abstract

We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by assuming that link weights evolve according to a geometric Brownian motion. Our model is verified by means of simulations and real world trade data. We show that the model correctly predicts the intensity and growth distribution of links, the size-variance relationships of the growth of link weights, the relationship between the degree and strength of nodes, as well as the scale-free structure of the network.