The Shortest Path to Network Geometry A Practical Guide to Basic Models and Applications

Real networks comprise hundreds to millions of interacting
elements and permeate all contexts, from technology to biology to society.
All of them display non-trivial connectivity patterns, including the
small-world phenomenon, making nodes to be separated by a small
number of intermediate links. As a consequence, networks present an
apparent lack of metric structure and are difficult to map. Yet, many
networks have a hidden geometry that enables meaningful maps in the
two-dimensional hyperbolic plane. The discovery of such hidden geometry
and the understanding of its role have become fundamental questions in
network science, giving rise to the field of network geometry. This Element
reviews fundamental models and methods for the geometric description of
real networks with a focus on applications of real network maps, including
decentralized routing protocols, geometric community detection, and the
self-similar multiscale unfolding of networks by geometric renormalization.