Asymptotic Normality of Degree Counts in a Preferential Attachment Model

TL;DR

This paper proves that degree counts in preferential attachment networks are asymptotically normal, enabling statistical inference on social network data despite its complex dependence structure.

Contribution

It establishes the asymptotic normality of degree counts in preferential attachment models using martingale methods, filling a gap for statistical inference in network analysis.

Findings

Degree counts are asymptotically normal in preferential attachment graphs.

Martingale techniques are effective for proving asymptotic properties.

Supports the use of classical statistical methods on network data.

Abstract

Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are asymptotically normal even though node or count based network data is nothing like classical data from independently replicated experiments. We therefore study asymptotic normality of degree counts for a sequence of growing simple undirected preferential attachment graphs. The methods of proof rely on identifying martingales and then exploiting the martingale central limit theorems.