Connectivity-Guided Sparsification of 2-FWL GNNs: Preserving Full Expressivity with Improved Efficiency

Higher-order Graph Neural Networks (HOGNNs) based on the 2-FWL test achieve superior expressivity by modeling 2- and 3-node interactions, but at $\mathcal{O}(n^3)$ computational cost. However, this computational burden is typically mitigated by existing efficiency methods at the cost of reduced expressivity. We propose \textbf{Co-Sparsify}, a connectivity-aware sparsification framework that eliminates \emph{provably redundant} computations while preserving full 2-FWL expressive power. Our key insight is that 3-node interactions are expressively necessary only within \emph{biconnected components} -- maximal subgraphs where every pair of nodes lies on a cycle. Outside these components, structural relationships can be fully captured via 2-node message passing or global readout, rendering higher-order modeling unnecessary. Co-Sparsify restricts 2-node message passing to connected components and 3-node interactions to biconnected ones, removing computation without approximation or sampling. We prove that Co-Sparsified GNNs are as expressive as the 2-FWL test. Empirically, on PPGN, Co-Sparsify matches or exceeds accuracy on synthetic substructure counting tasks and achieves state-of-the-art performance on real-world benchmarks (ZINC, QM9). This study demonstrates that high expressivity and scalability are not mutually exclusive: principled, topology-guided sparsification enables powerful, efficient GNNs with theoretical guarantees.

Tokenphormer: Structure-aware Multi-token Graph Transformer for Node Classification

Graph Neural Networks (GNNs) are widely used in graph data mining tasks. Traditional GNNs follow a message passing scheme that can effectively utilize local and structural information. However, the phenomena of over-smoothing and over-squashing limit the receptive field in message passing processes. Graph Transformers were introduced to address these issues, achieving a global receptive field but suffering from the noise of irrelevant nodes and loss of structural information. Therefore, drawing inspiration from fine-grained token-based representation learning in Natural Language Processing (NLP), we propose the Structure-aware Multi-token Graph Transformer (Tokenphormer), which generates multiple tokens to effectively capture local and structural information and explore global information at different levels of granularity. Specifically, we first introduce the walk-token generated by mixed walks consisting of four walk types to explore the graph and capture structure and contextual information flexibly. To ensure local and global information coverage, we also introduce the SGPM-token (obtained through the Self-supervised Graph Pre-train Model, SGPM) and the hop-token, extending the length and density limit of the walk-token, respectively. Finally, these expressive tokens are fed into the Transformer model to learn node representations collaboratively. Experimental results demonstrate that the capability of the proposed Tokenphormer can achieve state-of-the-art performance on node classification tasks.