Network geometry

Marián Boguñá, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Ángeles Serrano

Research output: Contribution to journalReview articlepeer-review

109 Scopus citations


Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity.

Original languageEnglish
Pages (from-to)114-135
Number of pages22
JournalNature Reviews Physics
Issue number2
StatePublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Limited.


S.H. thanks the Israel Science Foundation, ONR, the BIU Center for Research in Applied Cryptography and Cyber Security, NSF-BSF grant number 2019740, and DTRA grant number HDTRA-1-19-1-0016 for financial support. M.B. and M.A.S. acknowledge support from: a James S. McDonnell Foundation Scholar Award in Complex Systems; the ICREA Academia award, funded by the Generalitat de Catalunya; Agencia estatal de investigación project number PID2019-106290GB-C22/AEI/10.13039/501100011033; the Spanish Ministerio de Ciencia, Innovación y Universidades project number FIS2016-76830-C2-2-P (AEI/FEDER, UE); project Mapping Big Data Systems: embedding large complex networks in low-dimensional hidden metric spaces, Ayudas Fundación BBVA a Equipos de Investigación Científica 2017, and Generalitat de Catalunya grant number 2017SGR1064. D.K. acknowledges support from the NSF grant number IIS-1741355, and the ARO grant numbers W911NF-16-1-0391 and W911NF-17-1-0491.

FundersFunder number
NSF-BSF2019740, HDTRA-1-19-1-0016
National Science FoundationIIS-1741355
Office of Naval Research
Army Research OfficeW911NF-16-1-0391, W911NF-17-1-0491
James S. McDonnell Foundation
Ministerio de Ciencia, Innovación y UniversidadesFIS2016-76830-C2-2-P
Generalitat de Catalunya
Institució Catalana de Recerca i Estudis Avançats
Israel Science Foundation
European Regional Development Fund2017SGR1064
Agencia Estatal de InvestigaciónPID2019-106290GB-C22/AEI/10.13039/501100011033


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