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Series:   Elements in the Structure and Dynamics of Complex Networks

Higher-Order Networks

Published online by Cambridge University Press:  23 November 2021

Ginestra Bianconi
Ginestra Bianconi
Affiliation:
Queen Mary University of London

Summary

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.
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Keywords

Higher-order networksSimplicial complexesHigher-order dynamicsSimplicial network topology and geometryTopological data analysis
Type
Element
Information
Series: Elements in the Structure and Dynamics of Complex Networks
Online ISBN: 9781108770996
Publisher: Cambridge University Press
Print publication: 23 December 2021

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