Analytic Solution to Clustering Coefficients on Weighted Networks

TL;DR

This paper derives an analytical expression for the clustering coefficient in weighted networks, specifically BBV networks, revealing its dependence on node degree and strength, and validating results with numerical simulations.

Contribution

It provides the first analytical solutions for clustering coefficients in BBV weighted networks, enhancing understanding of their topological features.

Findings

Clustering coefficient depends on node degree and strength.

Analytical solutions match numerical simulation results.

Improves understanding of weighted network topology.

Abstract

Clustering coefficient is an important topological feature of complex networks. It is, however, an open question to give out its analytic expression on weighted networks yet. Here we applied an extended mean-field approach to investigate clustering coefficients in the typical weighted networks proposed by Barrat, Barth\'elemy and Vespignani (BBV networks). We provide analytical solutions of this model and find that the local clustering in BBV networks depends on the node degree and strength. Our analysis is well in agreement with results of numerical simulations.