Asymptotic normality of in- and out-degree counts in a preferential attachment model. Issue 2 (3rd April 2017) - Wang, Tiandong; Resnick, Sidney I.
ABSTRACT: Preferential attachment in a directed scale-free graph is an often used paradigm for modeling the evolution of social networks. Social network data is usually given in a format allowing recovery of the number of nodes with in-degree i and out-degree j . Assuming a model with preferential attachment, formal statistical procedures for estimation can be based on such data summaries. Anticipating the statistical need for such node-based methods, we prove asymptotic normality of the node counts. Our approach is based on a martingale construction and a martingale central limit theorem.