In this note, we present the hyperbolic Menelaus theorem in the Poincaré disc of hyperbolic geometry. 2000 Mathematical Subject Classi…cation: 30F45, 20N99, 51B10, 51M10 Keywords and phrases: hyperbolic geometry, hyperbolic triangle, gyrovector 1. Introduction Hyperbolic Geometry appeared in the …rst half of the 19 century as an attempt to understand Euclid’s axiomatic basis of Geometry. It is ...

In this paper we consider the clustering coefficient, and function in a random graph model proposed by Krioukov et al. 2010. model, nodes are chosen randomly inside disk hyperbolic plane two connected if they at most certain distance from each other. It has been previously shown that various properties associated with complex networks, including power-law degree distribution, “short distances” ...