In recent years, graph neural networks (GNNs) have gained significant attention for node classification tasks on graph-structured data. However, traditional GNNs primarily focus on adjacency relationships between nodes, often overlooking the role-based characteristics that can provide complementary insights for learning expressive node representations. Existing frameworks for extracting role-based features are largely unsupervised and often fail to translate effectively into downstream predictive tasks. To address these limitations, we propose a hypergraph neural network with a state space model (HGMN). The model integrates role-aware representations into GNNs by combining hypergraph construction with state-space modeling in a principled manner. HGMN employs hypergraph construction techniques to capture higher-order relationships and leverages a learnable mamba transformer mechanism to fuse role-based and adjacency-based embeddings. By exploring two distinct hypergraph construction strategies, degree-based and neighborhood-based, the framework reinforces connectivity among nodes with structural similarity, thereby enriching the learned representations. Furthermore, the inclusion of hypergraph convolution layers enables the model to account for complex dependencies within hypergraph structures. To alleviate the over-smoothing problem encountered in deeper networks, we incorporate residual connections, which improve stability and promote effective feature propagation across layers. Comprehensive experiments on benchmark datasets including OGB, ACM, DBLP, IIP TerroristRel, Cora, Citeseer, and Pubmed demonstrate that HGMN consistently outperforms strong baselines in node classification tasks. These results support the claim that explicitly incorporating role-based features within a hypergraph framework offers tangible benefits for node classification tasks.

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for matching large-scale graphs. Iterated line graphs are introduced for the first time to describe such high-order information, based on which we present a new graph matching method, called High-order Graph Matching Network (HGMN), to learn not only the local structural correspondence, but also the hyperedge relations across graphs. We theoretically prove that iterated line graphs are more expressive than graph convolution networks in terms of aligning nodes. By imposing practical constraints, HGMN is made scalable to large-scale graphs. Experimental results on a variety of settings have shown that, HGMN acquires more accurate matching results than the state-of-the-art, verifying our method effectively captures the structural similarity across different graphs.

While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to deep graph similarity learning. Recent work has considered either global-level graph-graph interactions or low-level node-node interactions, ignoring the rich cross-level interactions (e.g., between nodes and a whole graph). In this paper, we propose a Hierarchical Graph Matching Network (HGMN) for computing the graph similarity between any pair of graph-structured objects. Our model jointly learns graph representations and a graph matching metric function for computing graph similarities in an end-to-end fashion. The proposed HGMN model consists of a node-graph matching network for effectively learning cross-level interactions between nodes of a graph and a whole graph, and a siamese graph neural network for learning global-level interactions between two graphs. Our comprehensive experiments demonstrate that HGMN consistently outperforms state-of-the-art graph matching network baselines for both classification and regression tasks.