Abstract The hyperbolic random geometric graph was introduced by Krioukov et al. ( Phys. Rev. E 82 , 2010). Among many equivalent models for the space, we study d -dimensional Poincaré ball $d\ge 2$ ), with a general connectivity radius. While phase transitions are known expectation asymptotics of certain subgraph counts, very little is about second-order results. Two distinguishing characteris...

Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Even though there exist numerous nonequivalent definitions of graph curvature, none known converge in any limit traditional definition curvature a Riemannian manifold. Here we show that Ollivier random geometric graphs manifold converges the continuum Ricci underlying manifold, but only if properly ...

one of the conventional methods for temporary support of tunnels is to use steel sets with shotcrete. the nature of a temporary support system demands a quick installation of its structures. as a result, the spacing between steel sets is not a fixed amount and it can be considered as a random variable. hence, in the reliability analysis of these types of structures, the selection of an appropri...