SAC-Net: Structure-Aware Collaborative Network for Graph Similarity Computation

Abstract Graph Similarity Computation (GSC) is a core task in graph analysis. However, current mainstream GNN-based similarity models still suffer from two fundamental bottlenecks. First, constrained by the inherent mechanism of recursive local aggregation, namely the 1-Weisfeiler–Lehman (1-wl) test, these models primarily measure similarity by aligning local structures, while struggling to capture long-range dependencies and overall topological configurations. Second, the simplified treatment of edge features prevents them from fully exploiting fine-grained semantic interactions between nodes. To address these challenges, this paper pro-poses Structure-Aware Collaborative Network (SAC-Net), an end-to-end framework that leverages structural information to unify global contexts with local affinities. Specifically, we design a Dynamic Structural Perception (DSP) backbone to establish a joint evolution paradigm for node, position, and edge features. By treating positional encodings as dynamic states, the model effectively captures long-range dependencies and overall topological configurations to maintain a robust global structural skeleton. Subsequently, this study introduce an Edge-Aware Fusion mechanism that leverages edge features as a bridge to adaptively integrate global and local structural information, thereby effectively addressing the alignment and integration of multi-granularity semantics. Extensive experiments on four real-world datasets demonstrate that SAC-Net effectively integrates global and local information, leading to more accurate graph similarity measurement.