Higher-Order Networks

Ginestra Bianconi (Queen Mary University of London)

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English

Cambridge University Press
23 December 2021

Discrete mathematics; Statistical physics; Mathematical physics; Maths for computer scientists

Series: Elements in the Structure and Dynamics of Complex Networks

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.

By: Ginestra Bianconi (Queen Mary University of London)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 228mm, Width: 152mm, Spine: 7mm
Weight: 228g
ISBN: 9781108726733
ISBN 10: 1108726739
Series: Elements in the Structure and Dynamics of Complex Networks
Pages: 75
Publication Date: 23 December 2021
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

1. The relevance of higher-order networks in network science; 2. Combinatorial and statistical properties of simplicial complexes; 3. Simplicial network topology; 4. Simplicial network geometry; 5. Emergent geometry; 6. Higher-order dynamics: synchronization; 7. Higher-order dynamics: percolation; 8. Higher-order dynamics: contagion models; 9. Outlook; References.