DsrFGW Improves Graph Matching with Diffusion-Enabled Optimal Transport

Traditional graph comparison methods like Gromov-Wasserstein and its variants often struggle with sparse, noisy, or partially observed graphs, despite their ability to capture structural information. This limitation arises because they may not adequately account for how information propagates within a graph. Researchers propose Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel approach that enhances graph comparison by incorporating diffusion processes. Inspired by the idea that similar graphs facilitate similar information transmission, DsrFGW allows information to propagate across nodes, thereby capturing both local and global structural patterns more effectively while reducing sensitivity to noise or missing edges. Extensive evaluations across 36 synthetic graph matching tasks demonstrated DsrFGW's consistent superiority over existing methods like srFGW. It achieved significant accuracy improvements and dramatic gains in Adjusted Rand Index (ARI), particularly in medium-difficulty scenarios where srFGW often performed worse than random. DsrFGW also improved clustering quality in 92% of noisy synthetic tasks, establishing it as a robust framework for graph comparison under structural uncertainty.