Nonlinear PageRank Problem for Local Graph Partitioning

TL;DR

This paper introduces a nonlinear generalization of PageRank for local graph partitioning, utilizing the Moore-Penrose inverse and Levenberg-Marquardt method to effectively identify local clusters with high accuracy.

Contribution

It develops a novel nonlinear PageRank model and a numerical solution strategy that outperforms existing algorithms in local graph clustering tasks.

Findings

Successfully identifies low conductance local clusters

Recovers local clusters with higher accuracy than state-of-the-art methods

Demonstrates effectiveness on both synthetic and real-world graphs

Abstract

A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a strategy for obtaining a numerical solution to the generalised problem. Sets of vertices are formed according to the ranking supplied by the solution, and a conductance criterion decides upon the set that best represents the cluster around a starting vertex. Experiments on both synthetic and real-world inspired graphs demonstrate the capability of the approach to not only produce low conductance sets, but to also recover local clusters with an accuracy that consistently surpasses state-of-the-art algorithms.