Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms

Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research shows that topology-preserving coarsening methods maintain GNN performance on coarsened graphs but suffer 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.

This paper proposes a scalable topology-preserving method for reducing large networks. The key idea is to identify nodes and links that are structurally redundant and can be safely removed or merged while preserving important topological features, e.g., connected components and rings. Compared with previous topology-preserving methods that rely on expensive exhaustive search, our method is much more efficient and can handle larger networks. We also show that the reduced networks can be used to train graph learning models faster while maintaining strong prediction accuracy. Our results suggest that preserving topology is an effective way to make large-scale network learning both efficient and reliable.