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Asymptotic Normality of Degree Counts in a Preferential Attachment Model

Author
Resnick, Sidney; Samorodnitsky, Gennady
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.
Sponsorship
S. Resnick and G. Samorodnitsky were supported by Army MURI grant
W911NF-12-1-0385 to Cornell University
Date Issued
2015-04-28Subject
power law; degree counts; preferential attachment; random graphs
Type
technical report