Seeded PageRank Solution Paths

TL;DR

This paper introduces a fast, approximate method to compute PageRank diffusion solution paths across all regularization levels, revealing multi-scale cluster structures in large networks efficiently.

Contribution

It proposes a novel algorithm for efficiently approximating PageRank solution paths for all parameters, enabling multi-scale clustering analysis in large networks.

Findings

Method runs in time independent of network size.

Successfully applied to networks with up to 2 billion edges.

Reveals multi-scale cluster structures effectively.

Abstract

We study the behavior of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities) and also large macro-scale clusters by varying a parameter that has a dual-interpretation as an accuracy bound and as a regularization level. We propose a new method that quickly approximates the result of the diffusion for all values of this parameter. Our method efficiently generates an approximate $\textit{solution path}$ or $\textit{regularization path}$ associated with a PageRank diffusion, and it reveals cluster structures at multiple size-scales between small and large. We formally prove a runtime bound on this method that is independent of the size of the network, and we investigate multiple optimizations to our method that can be more practical in some settings. We demonstrate that these methods identify refined clustering structure on a number of real-world networks with up to 2 billion edges.