Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle

TL;DR

This paper introduces NOPE, a novel graph coarsening method based on a non-selfishness principle, achieving significant speedups and comparable or better performance than existing methods.

Contribution

The paper proposes a non-selfishness based graph coarsening technique, NOPE, with linear memory and near-linear complexity, and a faster variant NOPE* for high-degree nodes.

Findings

NOPE* achieves 1.8-10× speedup over NOPE.

NOPE* surpasses most baselines in speed and accuracy.

Learning on coarsened graphs maintains or improves performance.

Abstract

Graph coarsening is a graph dimensionality reduction technique that aims to construct a smaller and more tractable graph while preserving the essential structural and semantic properties of the original graph. However, most existing methods rely on pair-wise similarity matching, where each node independently searches for its best partner based on global information. This selfishness matching paradigm incurs substantial computational and memory overhead. To address this problem, we shift to a non-selfishness principle that prioritizes the collective interference of neighborhood in coarsening, and propose an efficient method named NOPE, which achieves linear memory consumption and near-linear computational complexity in the number of nodes. Furthermore, we derive a faster variant NOPE*, which reduces O(\delta \dot d) interference evaluation to O(d) based on the local isotropy assumption, and consequently alleviates the computational bottleneck for high-degree nodes. Experimental results show that NOPE* achieves 1.8-10\times speedup over NOPE and surpass almost all baselines with 1-3 orders of magnitude acceleration. Meanwhile, learning on coarsened graphs yields comparable performance to original graphs, and can even show superior performance over LLM-based graph reasoning owing to compact graph information. The code can be available at https://github.com/dazonglian/NOPE-main.