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Series:   Elements in the Structure and Dynamics of Complex Networks

The Shortest Path to Network Geometry

A Practical Guide to Basic Models and Applications

Published online by Cambridge University Press:  02 December 2021

M. Ángeles Serrano  and
Marián Boguñá
M. Ángeles Serrano
Affiliation:
University of Barcelona, University of Barcelona Institute of Complex Systems (UBICS) and Catalan Institution for Research and Advanced Studies (ICREA)
Marián Boguñá
Affiliation:
University of Barcelona and University of Barcelona Institute of Complex Systems (UBICS)

Summary

Real networks comprise from 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.
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Keywords

network geometrymapping techniquesnavigabilitycommunity detectionrenormalization
Type
Element
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Series: Elements in the Structure and Dynamics of Complex Networks
Online ISBN: 9781108865791
Publisher: Cambridge University Press
Print publication: 06 January 2022

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The Shortest Path to Network Geometry
  • M. Ángeles Serrano, University of Barcelona, University of Barcelona Institute of Complex Systems (UBICS) and Catalan Institution for Research and Advanced Studies (ICREA), Marián Boguñá, University of Barcelona and University of Barcelona Institute of Complex Systems (UBICS)
  • Online ISBN: 9781108865791
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The Shortest Path to Network Geometry
  • M. Ángeles Serrano, University of Barcelona, University of Barcelona Institute of Complex Systems (UBICS) and Catalan Institution for Research and Advanced Studies (ICREA), Marián Boguñá, University of Barcelona and University of Barcelona Institute of Complex Systems (UBICS)
  • Online ISBN: 9781108865791
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The Shortest Path to Network Geometry
  • M. Ángeles Serrano, University of Barcelona, University of Barcelona Institute of Complex Systems (UBICS) and Catalan Institution for Research and Advanced Studies (ICREA), Marián Boguñá, University of Barcelona and University of Barcelona Institute of Complex Systems (UBICS)
  • Online ISBN: 9781108865791
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