higher-order networks.pdf
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BIANCONI
Higher-Order 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 become 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 Element 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.
About the series
This cutting-edge new series provides
authoritative and detailed coverage
of the underlying theory of complex
networks, specifically their structure and
dynamical properties. Each Element within
the series will focus upon one of three
primary topics: static networks, dynamical
networks and numerical/computing
network resources.
Series editors
Guido Caldarelli
Ca’ Foscari
University of
Venice
The Structure and Dynamics
of Complex Networks
ISSN 2516-5763 (online)
ISSN 2516-5755 (print)
Higher-Order
Networks
An Introduction to
SimplicialComplexes
Ginestra Bianconi
Cover image: jivacore/Shutterstock
Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781108770996
Downloaded from https://www.cambridge.org/core. China University of Mining and Technology, on 26 Nov 2021 at 09:12:02, subject to the
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