Graph Alignment and Matching

Instead of viewing graphs in isolation, many real-world problems need finding how two or more networks correspond to one another. This chapter focuses on graph alignment and matching as the key techniques for discovering such cross-graph relationships. It explains the purpose of aligning nodes, edges, and substructures across graphs, supported by initive examples and use cases. Both exact and inexact matching approaches are examined along with global and local alignment strategies. The chapter then introduces mathematical and learning-based solutions, including graph embeddings with distance minimization, Gromov-Wasserstein distance, contrastive learning, and deep graph matching networks such as DGMC. The chapter demonstrates how alignment enables knowledge transfer and consistency across networks using case studies.