Assortativity in Generalized Preferential Attachment Models

TL;DR

This paper investigates the assortativity properties of a broad class of preferential attachment models, extending previous analyses of degree distribution and clustering by focusing on neighbor degree correlations.

Contribution

It provides a detailed analysis of assortativity in PA-class models, including the behavior of neighbor degree correlations, which was not previously explored.

Findings

Degree distribution follows a power law in PA-class models.

Global and local clustering coefficients are characterized.

Assortativity behavior of neighbor degrees is analyzed.

Abstract

In this paper, we analyze assortativity of preferential attachment models. We deal with a wide class of preferential attachment models (PA-class). It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global and the average local clustering coefficients were analyzed. We expand these results by analyzing the assortativity property of the PA-class of models. Namely, we analyze the behavior of $d_{nn}(d)$ which is the average degree of a neighbor of a vertex of degree $d$.