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Nonstandard regular variation of the in-degree and the out-degree in the preferential attachement model

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Abstract

For the directed edge preferential attachment network growth model studied by Bollobas et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular variation is non-standard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.

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The research of the authors was supported by MURI ARO Grant W911NF-12-10385 to Cornell University

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2014-06-25

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multivariate heavy tails; preferential attachment model; scale free networks

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technical report

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