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Gradient and Harnack-type estimates for PageRank

Published online by Cambridge University Press:  03 September 2020

Paul Horn  and
Lauren M. Nelsen Open the ORCID record for Lauren M. Nelsen [Opens in a new window]
Paul Horn
Affiliation:
University of Denver, Denver, CO80208, USA (e-mail: paul.horn@du.edu)
Lauren M. Nelsen*
Affiliation:
University of Indianapolis, Indianapolis, IN46227, USA
*
*Corresponding author. Email: nelsenl@uindy.edu
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Abstract

Personalized PageRank has found many uses in not only the ranking of webpages, but also algorithmic design, due to its ability to capture certain geometric properties of networks. In this paper, we study the diffusion of PageRank: how varying the jumping (or teleportation) constant affects PageRank values. To this end, we prove a gradient estimate for PageRank, akin to the Li–Yau inequality for positive solutions to the heat equation (for manifolds, with later versions adapted to graphs).

Keywords

PageRankdiscrete curvaturerandom walksgradient estimate
Type
Research Article
Information
Network Science , Volume 9 , Special Issue S1: Complex Networks 2019 , October 2021 , pp. S4 - S22
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Special Issue Editor: Hocine Cherifi

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