The focus of this work is the asymptotic analysis of the tail distribution of Google’s PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich–Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i.d. copies of the attracting endogenous solution to a branching distributional fixed-point equation. In addition, we provide the asymptotic tail behavior of the limit and use it to explain the effect that in-degree/out-degree correlations in the underlying graph can have on the qualitative performance of PageRank.
The author would like to thank two anonymous referees whose comments helped improve the readability of the paper.
"PageRank’s behavior under degree correlations." Ann. Appl. Probab. 31 (3) 1403 - 1442, June 2021. https://doi.org/10.1214/20-AAP1623