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.
Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers. We show that several existing scalable approaches can be written as structured modifications of the GNN propagation matrix, providing a unified perspective that exposes their respective limitations. In particular, graph coarsening replaces it by a low-rank approximation that enables spectral guarantees but assigns uniform representations to clustered nodes, while Cluster-GCN restricts the propagation matrix to intra-cluster connections that allow efficient batching but sever long-range information. These are complementary failures of the \emph{same} decomposition of the graph into groups of nodes. To obtain the best of both worlds, we propose \textbf{CoRe-GNN}, which performs both propagations in parallel at each layer: a coarsened inter-cluster term capturing long-range structure, and a local intra-cluster term preserving per-node discriminability. We prove that CoRe-GNN inherits analogous approximation guarantees to those of graph coarsening, and introduce a natural cluster-based \emph{batching scheme} that scales to graphs with millions of nodes. On node classification benchmarks spanning homophilic, heterophilic, large-scale, and long-range graphs, CoRe-GNN outperforms both graph coarsening and Cluster-GCN baselines. Notably, CoRe-GNN reaches competitive accuracy on \emph{long-range} tasks, while remaining memory-efficient through batching.
Coarsening-based training for graph neural networks (GNNs), i.e.\ training on coarsened graphs rather than the original large ones, has become a promising direction for scaling GNNs to massive graphs. However, prior work has been evaluated almost exclusively on \textit{homophilic} graphs, leaving the more challenging \textit{heterophilic} settings underexplored. We show, both empirically and theoretically, that existing coarsening-based training methods suffer significant performance degradation on heterophilic graphs due to inevitable loss of graph information during coarsening. To address this, we propose {\bf A}daptive {\bf C}omplementary {\bf E}nhancement, a plug-and-play, model-agnostic strategy that reintegrates the information discarded in coarsening: ACE learns a projector for re-constructing original node features and applies \textit{anisotropic structural regularization} to embed local heterophily. We further adopt \textit{homoscedastic uncertainty weighting} to adaptively balance the combined training objective of primary coarsened-graph training loss and full-graph auxiliary loss with augmented node features re-constructed by the heterophily-aware projector. Extensive experiments show that ACE drives consistent gains on heterophilic benchmarks while preserving competitive results on homophilic graphs with minimal computational overhead. Code is available at the GitHub repository: https://github.com/vasile-paskardlgm/ACE.
Graph self-supervised learning typically relies on large-scale unlabeled datasets, heavily inflating computational costs. However, empirical evidence suggests that these datasets contain substantial redundancy-our analysis reveals that uniformly subsampling 50% of graphs retains over 96% of downstream performance. To exploit this redundancy, we introduce GraphSculptor for pre-training coreset construction. Unlike methods dependent on additional training-time signals or limited solely to topological statistics, GraphSculptor provides a label-free solution that constructs coresets via two complementary perspectives: intrinsic structure and contextual semantics. Concretely, structural diversity is quantified using intrinsic graph statistics, yielding a structural feature vector for each graph, while semantic diversity is captured by utilizing a pre-trained language model to encode descriptions generated via graph-to-text. GraphSculptor integrates these signals into a unified metric space and performs cluster-aware selection to preserve joint structural-semantic diversity. We further derive a theoretical bound on the loss gap between coreset and full-data pre-training, offering theoretical motivation for our selection formulation. Extensive experiments demonstrate that GraphSculptor effectively sculpts the dataset: a 10% coreset achieves 99.6% of full-data performance while reducing pre-training time by nearly 90%, offering a scalable solution for data-efficient graph pre-training.