Asymptotic normality of in- and out-degree counts in a preferential attachment model. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Wang, Tiandong; Resnick, Sidney I.
• Is Part Of: Stochastic models. Volume 33:Issue 2(2017)
• Page Start: 229
• Page End: 255
• Publication Date: 2017-04-03
• Subjects: Asymptotic normality -- in-degree -- multivariate heavy tails -- out-degree -- power laws -- preferential attachment -- random graphs; 05C20 -- 60G70 -- 28A33 -- 60G51; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2016.1256219
• Languages: English
• ISSNs: 1532-6349

Abstract

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.