Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle

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\cdot 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.

Lay Summary Large graphs, such as social or citation networks, are expensive to process because they contain enormous numbers of nodes and connections. Existing graph coarsening methods compress graphs by letting each node independently search for its best match, but this selfish strategy requires costly global comparisons and large memory usage. We propose \texttt{NOPE}, a new graph coarsening method based on a non-selfish principle that considers the collective influence of local neighborhoods instead of isolated node matching. We further develop \texttt{NOPE}, a faster variant that reduces computation for high-degree nodes and improves scalability. Experiments show that NOPE is often 1–3 orders of magnitude faster than existing methods while maintaining comparable learning performance on the coarsened graphs. In some cases, the compact coarsened graphs even outperform LLM-based graph reasoning approaches.