PageRank's behavior under degree-degree correlations

TL;DR

This paper analyzes the asymptotic distribution of PageRank scores on large scale-free directed networks, revealing how degree correlations influence PageRank's behavior and tail distribution.

Contribution

It provides a rigorous convergence result for PageRank distribution on complex networks and characterizes the impact of degree correlations on PageRank's tail behavior.

Findings

PageRank distribution converges to a limit described by a branching fixed-point equation

Degree-degree correlations significantly affect PageRank's tail distribution

Asymptotic tail behavior explains qualitative differences in PageRank performance

Abstract

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.