SimGAT: structure-aware graph attention network with multi-scale structural embedding

Graph neural networks (GNNs) have achieved strong performance in graph representation learning by integrating node attributes with local topology. However, most existing GNNs rely on local message passing, limiting their ability to capture global structural similarity and higher-order topological dependencies. Although SimRank offers a classical measure of structural-context similarity, its pairwise scalar outputs and quadratic computational cost make direct integration into node-level GNN frameworks impractical. Moreover, conventional SimRank suffers from expressive limitations: zero similarity in directed graphs and structural discrimination collapse in undirected or highly symmetric structures. To address these challenges, we propose SimGAT, a structure-aware graph attention model built on SimRank-derived structural embeddings. We first introduce SimRank2Vec, which converts multi-order SimRank propagation relationships into compact node-level representations through matrix factorization. The resulting embeddings alleviate the expressive limitations of conventional SimRank while providing a scalable structural representation for GNNs. SimGAT then computes structural similarity in the SimRank2Vec embedding space and injects it as a topological prior into the graph attention mechanism, enabling neighborhood aggregation to be jointly guided by node attributes and global structural relationships. Experiments on nine benchmark datasets, namely TwitchPT, TwitchRU, Texas, Cora, Citeseer, Photo, ACM, DBLP, and Film, demonstrate that SimRank2Vec improves structural representation quality, and that SimGAT achieves competitive and stable performance across node classification, community detection, and node representation visualization. The code is available at https://github.com/Chengda217/SimGAT .