Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle

2026-05-13

AI Summary

Existing graph coarsening methods rely on node-wise selfish pairing strategies, resulting in high computational and memory overhead. This work proposes NOPE, a non-selfish graph coarsening framework that models collective neighborhood interference to achieve near-linear time complexity and linear memory consumption while preserving coarsening quality. Building upon a local isotropy assumption, the authors further introduce NOPE*, a variant that reduces the complexity of higher-order interference evaluation from O(δ·d) to O(d). Experimental results demonstrate that NOPE* accelerates NOPE by 1.8–10× and outperforms baseline methods by one to three orders of magnitude in speed, while maintaining learning performance on coarsened graphs that matches or exceeds that on original graphs and even large language model–based graph inference outcomes.

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(δ\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.

Problem

• graph coarsening
• selfishness matching
• computational overhead
• memory overhead
• dimensionality reduction

Innovation

• graph coarsening
• non-selfishness principle
• linear complexity
• neighborhood interference
• efficient graph learning