Higher-Order Networks
Published on 15. December 2021
978-1-108-80542-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
File size
6,62 MB
ISBN-13
978-1-108-80542-1 (9781108805421)
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Schweitzer Classification
Other editions
Additional editions
Book
12/2021
Cambridge University Press
€38.40
Shipment within 15-20 days
Person
Content
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.
