Graph Isomorphism

Graph isomorphism, the problem of determining whether two graphs are structurally identical, is a fundamental challenge in computer science with implications for diverse fields. Current research focuses on developing more expressive graph neural networks (GNNs) and algorithms, often leveraging variations of the Weisfeiler-Lehman test and incorporating techniques like graph partitioning and subgraph analysis to improve their ability to distinguish non-isomorphic graphs. These advancements are crucial for enhancing the performance of GNNs in various applications, including chemical molecule analysis, drug discovery, and social network analysis, where accurate graph comparisons are essential. Furthermore, research explores connections between graph isomorphism and other mathematical frameworks, such as optimal transport and Gromov-Wasserstein distances, to develop novel distance metrics and algorithms.