Method Detecting Overlapping Structures in Bipartite Graphs via SBM
摘要
This article proposes a novel method for detecting overlapping communities in bipartite graphs using stochastic block models. Motivated by the analysis of social structures in ancient Egyptian kingdoms, the method addresses limitations of existing approaches that either ignore bipartite structure or handle only disjoint communities. The proposed obSBM method extends mixed membership models to naturally incorporate both overlapping memberships and bipartite constraints. Performance evaluation on synthetic bipartite networks demonstrates superior results compared to existing methods, particularly as community overlap increases. Real-world validation on Egyptian administrative data shows meaningful community structures, though detailed historical analysis is beyond this paper’s scope. Convergence is guaranteed through EM algorithm analysis, with formal proof based on monotonic likelihood increase and properties of the objective function.