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

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