PageRank on inhomogeneous random digraphs

Abstract

We study the typical behavior of Google’s PageRank algorithm on inhomogeneous random digraphs, including directed versions of the Erdős–Rényi model, the Chung–Lu model, the Poissonian random graph and the generalized random graph. Specifically, we show that the rank of a randomly chosen vertex converges weakly to the attracting endogenous solution to the stochastic fixed-point equation R=D∑i=1NCiRi+Q, where (N,Q,{Ci}i≥1) is a real-valued vector with N∈N, and the {Ri} are i.i.d. copies of R, independent of (N,Q,{Ci}i≥1); =D denotes equality in distribution. This result provides further evidence of the power-law behavior of PageRank on graphs whose in-degree distribution follows a power law.