Asymptotic normality of in- and out-degree counts in a preferential attachment model |
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Authors: | Tiandong Wang Sidney I. Resnick |
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Affiliation: | School of Operations Research and Information Engineering, Cornell University, Ithaca, New York, USA |
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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. |
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Keywords: | Asymptotic normality in-degree multivariate heavy tails out-degree power laws preferential attachment random graphs |
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