June 2021 PageRank’s behavior under degree correlations
Mariana Olvera–Cravioto
Author Affiliations +
Ann. Appl. Probab. 31(3): 1403-1442 (June 2021). DOI: 10.1214/20-AAP1623


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.


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Mariana Olvera–Cravioto. "PageRank’s behavior under degree correlations." Ann. Appl. Probab. 31 (3) 1403 - 1442, June 2021. https://doi.org/10.1214/20-AAP1623


Received: 1 September 2019; Revised: 1 August 2020; Published: June 2021
First available in Project Euclid: 23 June 2021

MathSciNet: MR4278789
zbMATH: 1477.05173
Digital Object Identifier: 10.1214/20-AAP1623

Primary: 05C80 , 60J80
Secondary: 41A60 , 60B10

Keywords: complex networks , degree-correlations , Directed random graphs , distributional fixed-point equations , PageRank , power laws , ranking algorithms , Weighted branching processes

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.31 • No. 3 • June 2021
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