Block Model

Block models are statistical frameworks used to identify underlying community structures within networks or data matrices, aiming to uncover hidden groupings of nodes or variables exhibiting similar patterns. Current research emphasizes robust and efficient algorithms, including spectral clustering, semidefinite programming, and variational methods, often applied within stochastic block models (SBMs) and their extensions (e.g., degree-corrected, hierarchical, and mixed-membership SBMs) to handle diverse data types and network complexities. These advancements improve community detection accuracy and scalability, impacting fields like social network analysis, bioinformatics, and recommendation systems by enabling more precise and insightful analyses of complex relationships. The development of optimal algorithms and theoretical guarantees for exact community recovery under various model assumptions remains a key focus.