Mathematical Properties of the Hyperbolicity of Circulant Networks

Abstract

The first works on Gromov hyperbolic spaces deal with finitely generated groups. Initially, Gromov spaces were applied to the study of automatic groups in the science of computation; indeed, hyperbolic groups are strongly geodesically automatic; that is, there is an automatic structure on the group. Besides, hierarchical networks have been found to have hidden hyperbolic structure. Forastudyofotherparametersincomplexnetworks,see. The concept of hyperbolicity appears also in discrete mathematics, algorithms, and networking. For example, it has been shown empirically in that the Internet topology embeds with better accuracy into a hyperbolic space tan into an Euclidean space of comparable dimension; the same holds for many complex networks.