Graph Matching

Graph matching studies how to align nodes and edges across graphs, from finding exact isomorphisms and common subgraphs to estimating graph edit distance or matching noisy, partially observed structures. Approaches include combinatorial search and convex relaxations, optimal-transport methods such as Sinkhorn and Gromov–Wasserstein, and learned models using graph neural networks, attention, or semantic and geometric cues. Applications range from molecular comparison and scene registration to robotics, image retrieval, and structured-data evaluation. A central tension is achieving accurate, globally consistent matches while scaling to large graphs and generalizing across domains, especially when correspondences are ambiguous or supervision is limited.