Clustering of correlated networks

TL;DR

This paper derives formulas for clustering metrics in correlated networks, enabling analysis of their clustering structure based on degree correlations.

Contribution

It provides new analytical formulas for clustering coefficients in networks with arbitrary degree correlations.

Findings

Formulas for clustering coefficient and local clustering.

Ability to analyze clustering based on degree correlations.

Framework for understanding network clustering properties.

Abstract

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine the nature of the clustering of a network.