## 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.