Random Hyperbolic Graphs with Arbitrary Mesoscale Structures
Real-world networks exhibit both geometric properties—such as sparsity, small-worldness, power-law degree distribution, and high clustering—and non-geometric mesoscale structures—e.g., arbitrary community mixing patterns. Classical Random Hyperbolic Graphs (RHGs) model only node similarity and popularity, but their strict triangle inequality constraint prevents accurate representation of non-geometric inter-community connections. To address this, we propose the Random Hyperbolic Block Model (RHBM), the first model to explicitly integrate block structure into hyperbolic geometry under a maximum-entropy framework. RHBM decouples intra- and inter-block similarity, enabling violation of the triangle inequality to capture realistic inter-community links. Experiments demonstrate that RHBM preserves RHG’s macroscopic properties while precisely and controllably reproducing target community structures—outperforming RHG significantly on synthetic benchmarks.