Mean Field Analysis of Personalized PageRank with Implications for Local Graph Clustering

TL;DR

This paper provides a mean-field theoretical analysis of Personalized PageRank on random graphs with planted subgraphs, exploring its concentration properties, parameter optimization, and implications for local graph clustering.

Contribution

It introduces a mean-field model for Personalized PageRank on Erdős-Rényi graphs with planted subgraphs, analyzing parameter effects and limitations for clustering tasks.

Findings

Personalized PageRank concentrates around the mean-field value in certain regimes.

Optimal damping factors can be identified for improved clustering performance.

Theoretical insights clarify when Personalized PageRank is effective for local clustering.

Abstract

We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi random graph containing a denser planted Erdos-Renyi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate around the mean-field value. We also study the optimization of the damping factor, the only parameter in Personalized PageRank. Our theoretical results help to understand the applicability of Personalized PageRank and its limitations for local graph clustering.