Asymptotic Normality of Degree Counts in a Preferential Attachment Model
Resnick, Sidney; Samorodnitsky, Gennady
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.
S. Resnick and G. Samorodnitsky were supported by Army MURI grant W911NF-12-1-0385 to Cornell University
power law; degree counts; preferential attachment; random graphs