  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.
