Nonstandard regular variation of the in-degree and the out-degree in the preferential attachement model
Samorodnitsky, Gennady; Resnick, Sidney; Towsley, Don; Davis, Richard; Willis, Amy; Wan, Phyllis
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.
multivariate heavy tails; preferential attachment model; scale free networks