  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.
