Graph Sparsification

Graph sparsification studies how to remove edges while keeping important properties such as connectivity, Laplacian spectra, signal propagation, or downstream task performance. Methods include effective-resistance sampling and other spectral techniques, spanning-tree and nearest-neighbor constructions, and learned or task-aware edge selection. Researchers evaluate sparse graphs in settings such as GNN node classification, semi-supervised learning, routing, and traveling-salesperson optimization, measuring both accuracy or solution quality and savings in memory or computation. A central tension is that preserving global structure does not always preserve task-specific behavior: sparsity, propagation fidelity, and downstream performance can trade off, especially across different graph types and tasks.