Local Clustering Coefficient in Generalized Preferential Attachment Models

TL;DR

This paper investigates the local clustering coefficient in a broad class of preferential attachment models, extending previous work on degree distribution and global clustering to local clustering behavior.

Contribution

It provides an analysis of the local clustering coefficient C(d) for vertices of degree d within the PA-class of models, expanding understanding of clustering in these networks.

Findings

Derived the behavior of C(d) for PA-class models

Extended previous results on global clustering

Confirmed power-law degree distribution in models

Abstract

In this paper, we analyze the local clustering coefficient of preferential attachment models. A general approach to preferential attachment was introduced in earlier, where a wide class of models (PA-class) was defined in terms of constraints that are sufficient for the study of the degree distribution and the clustering coefficient. It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global clustering coefficient was analyzed and a lower bound for the average local clustering coefficient was obtained. We expand the results by analyzing the local clustering coefficient for the PA-class of models. Namely, we analyze the behavior of C(d) which is the average local clustering for the vertices of degree d.