Approximate Graph Propagation

TL;DR

This paper introduces Approximate Graph Propagation (AGP), a unified randomized algorithm that efficiently computes multiple node proximity measures and GNN features with theoretical guarantees, enhancing scalability on large graphs.

Contribution

AGP is a novel unified algorithm that approximates various proximity queries and GNN features with bounded error and near-optimal time complexity.

Findings

AGP effectively computes multiple proximity measures with bounded error.

AGP significantly improves GNN scalability on large graphs.

Empirical results on billion-edge graph demonstrate AGP's efficiency and accuracy.

Abstract

Efficient computation of node proximity queries such as transition probabilities, Personalized PageRank, and Katz are of fundamental importance in various graph mining and learning tasks. In particular, several recent works leverage fast node proximity computation to improve the scalability of Graph Neural Networks (GNN). However, prior studies on proximity computation and GNN feature propagation are on a case-by-case basis, with each paper focusing on a particular proximity measure. In this paper, we propose Approximate Graph Propagation (AGP), a unified randomized algorithm that computes various proximity queries and GNN feature propagation, including transition probabilities, Personalized PageRank, heat kernel PageRank, Katz, SGC, GDC, and APPNP. Our algorithm provides a theoretical bounded error guarantee and runs in almost optimal time complexity. We conduct an extensive experimental study to demonstrate AGP's effectiveness in two concrete applications: local clustering with heat kernel PageRank and node classification with GNNs. Most notably, we present an empirical study on a billion-edge graph Papers100M, the largest publicly available GNN dataset so far. The results show that AGP can significantly improve various existing GNN models' scalability without sacrificing prediction accuracy.