Asymptotic Normality of In- and Out-Degree Counts in a Preferential Attachment Model

TL;DR

This paper proves that in a directed preferential attachment model, the counts of nodes with specific in- and out-degrees follow an asymptotic normal distribution, supporting statistical inference in social network analysis.

Contribution

It establishes the asymptotic normality of node degree counts in a directed preferential attachment model using martingale methods, providing theoretical justification for statistical estimation.

Findings

Node degree counts are asymptotically normal.

Martingale construction is used for proof.

Supports statistical analysis of social networks.

Abstract

Preferential attachment in a directed scale-free graph is widely used to model the evolution of social networks. Statistical analyses of social networks often relies on node based data rather than conventional repeated sampling. For our directed edge model with preferential attachment, we prove asymptotic normality of node counts based on a martingale construction and a martingale central limit theorem. This helps justify estimation methods based on the statistics of node counts which have specified in-degree and out-degree.