The modularity of random graphs on the hyperbolic plane

Abstract Modularity is a quantity which has been introduced in the context of complex networks order to quantify how close network an ideal modular nodes form small interconnected communities that are joined together with relatively few edges. In this article, we consider on probabilistic model by Krioukov et al. (2010, Phys. Rev. E, 82, 036106). This views as expression hidden popularity hierarchies (i.e. higher up have more global reach), encapsulated underlying hyperbolic space. For certain parameters, was proved typical features observed such power law degree distribution, bounded average degree, clustering coefficient asymptotically away from zero and ultra-small distances. present work, investigate its modularity show that, regime, it converges one probability.