Fused Gromov-Wasserstein Alignment for Graph Edit Distance Computation and Beyond

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Abstract

Graph Edit Distance (GED) is a widely recognized metric for measuring graph similarity, yet its NP-complete nature poses challenges for fast and accurate computation. This paper introduces FGWAlign, an Optimal Transport (OT)-based approach for graph alignment and GED computation. We take the first step to theoretically demonstrate and that computing GED can be transformed into optimizing a particular OT variant—the Fused Gromov-Wasserstein distance. Tailored to the GED problem structure, we further implement three key enhancements to the standard FGW solver: (1) a random exploration scheme to better locate the global optimum, (2) a diverse projection strategy for post-processing the transportation plan to escape local optima, and (3) a novel extension to accommodate multi-relational graphs with edge labels. With O(| 𝑽 || 𝑬 |) time complexity and O(| 𝑽 | 2 ) space complexity, where | 𝑽 | and | 𝑬 | are the maximum number of nodes and edges between the two compared graphs, FGWAlign achieves a superior balance of efficiency, accuracy, and scalability. Empirical results show that, compared with 12 representative GED computation methods across different categories on 4 real-world graph datasets, FGWAlign reduces computation errors by over 80% and achieves 15-60 × speedup. It also demonstrates promising resutls on downstream applications including labeled graph alignment and graph-level anomaly detection, highlighting its versatility. FGWAlign opens up promising avenues for future applications in graph data management.