  Modularity is a quantity which has been introduced in the context of complex
networks in order to quantify how close a network is to an ideal modular
network in which the nodes form small interconnected communities that are
joined together with relatively few edges. In this paper, we consider this
quantity on a recent probabilistic model of complex networks introduced by
Krioukov et al. (Phys. Rev. E 2010).
  This model views a complex network as an expression of hidden hierarchies,
encapsulated by an underlying hyperbolic space. For certain parameters, this
model was proved to have typical features that are observed in complex networks
such as power law degree distribution, bounded average degree, clustering
coefficient that is asymptotically bounded away from zero, and ultra-small
typical distances. In the present work, we investigate its modularity and we
show that, in this regime, it converges to 1 in probability.
