Scalable Topology-Preserving Graph Coarsening with Graph Collapse

TL;DR

This paper introduces a scalable graph coarsening method that preserves topological features to maintain GNN performance, using algebraic topology concepts and efficient algorithms.

Contribution

It proposes STPGC, a novel topological graph coarsening approach with three algorithms, extending algebraic topology to improve efficiency and preserve GNN receptive fields.

Findings

STPGC effectively preserves topological features during coarsening.

The algorithms accelerate GNN training without sacrificing accuracy.

Experiments show improved efficiency and maintained predictive performance.

Abstract

Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research has shown that preserving topological features helps maintain the predictive performance of graph neural networks (GNNs) trained on the coarsened graph but suffers from exponential time complexity. To address these problems, we propose Scalable Topology-Preserving Graph Coarsening (STPGC) by introducing the concepts of graph strong collapse and graph edge collapse extended from algebraic topology. STPGC comprises three new algorithms, GStrongCollapse, GEdgeCollapse, and NeighborhoodConing based on these two concepts, which eliminate dominated nodes and edges while rigorously preserving topological features. We further prove that STPGC preserves the GNN receptive field and develop approximate algorithms to accelerate GNN training. Experiments on node classification with GNNs demonstrate the efficiency and effectiveness of STPGC.