Weighted Network Models Based on Local and Global Rules

TL;DR

This paper introduces two new evolving models for weighted complex networks that exhibit power-law distributions and tunable clustering and assortativity, supported by empirical evidence and extending previous models.

Contribution

It develops two novel weighted network models with similar mathematical frameworks, expanding on Barrat et al.'s work and capturing key network properties.

Findings

Models exhibit power-law degree, weight, and strength distributions.

Clustering coefficient C and degree assortativity r are tunable.

Empirical data supports the models' relevance.

Abstract

We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for example, the power-law distributions and evolution of degree, weight and strength. We also study the nontrivial clustering coefficient C and tunable degree assortativity coefficient r, depending on specific parameters. Most results are supported by present empirical evidences, and may provide us with a better description of the hierarchies and organizational architecture of weighted networks. Our models have been inspired by the weighted network model proposed by Alain Barrat et al. (BBV for short), and can be considered as a meaningful development of their original work.