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Higher-Order Systems

  • Book
  • © 2022

Overview

Editors:
  1. Federico Battiston

    1. Department of Network and Data Science, Central European University, Vienna, Austria

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    You can also search for this editor in PubMed   Google Scholar

  2. Giovanni Petri

    1. ISI Foundation, Turin, Italy

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    You can also search for this editor in PubMed   Google Scholar

  • Provides an introduction to and overview of the emerging field of networks beyond pairwise interactions
  • Includes simplicial complexes, hypergraphs, as well as other higher-order systems
  • Is an introductory book and state-of-the art overview of this rapidly emerging field

Part of the book series: Understanding Complex Systems (UCS)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-x
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  2. Graphs, Simplicial Complexes and Hypergraphs: Spectral Theory and Topology

    • Raffaella Mulas, Danijela Horak, Jürgen Jost
    Pages 1-58

  3. Random Simplicial Complexes: Models and Phenomena

    • Omer Bobrowski, Dmitri Krioukov
    Pages 59-96

  4. Persistent Homology: A Topological Tool for Higher-Interaction Systems

    • Francesco Vaccarino, Ulderico Fugacci, Sara Scaramuccia
    Pages 97-139

  5. Flow-Based Community Detection in Hypergraphs

    • Anton Eriksson, Timoteo Carletti, Renaud Lambiotte, Alexis Rojas, Martin Rosvall
    Pages 141-161

  6. Pattern Formation on Hypergraphs

    • Timoteo Carletti, Duccio Fanelli
    Pages 163-180

  7. Non-pairwise Interaction in Oscillatory Ensembles: from Theory to Data Analysis

    • Arkady Pikovsky, Michael Rosenblum
    Pages 181-195

  8. From Symmetric Networks to Heteroclinic Dynamics and Chaos in Coupled Phase Oscillators with Higher-Order Interactions

    • Peter Ashwin, Christian Bick, Ana Rodrigues
    Pages 197-216

  9. Explosive Synchronization and Multistability in Large Systems of Kuramoto Oscillators with Higher-Order Interactions

    • Per Sebastian Skardal, Alex Arenas
    Pages 217-232

  10. Multiorder Laplacian for Kuramoto Dynamics with Higher-Order Interactions

    • Maxime Lucas, Giulia Cencetti, Federico Battiston
    Pages 233-247

  11. The Master Stability Function for Synchronization in Simplicial Complexes

    • Lucia Valentina Gambuzza, Francesca Di Patti, Luca Gallo, Stefano Lepri, Miguel Romance, Regino Criado et al.
    Pages 249-267

  12. Geometry, Topology and Simplicial Synchronization

    • Ana Paula Millán, Juan G. Restrepo, Joaquín J. Torres, Ginestra Bianconi
    Pages 269-299

  13. Signal Processing on Simplicial Complexes

    • Michael T. Schaub, Jean-Baptiste Seby, Florian Frantzen, T. Mitchell Roddenberry, Yu Zhu, Santiago Segarra
    Pages 301-328

  14. Social Contagion on Higher-Order Structures

    • Alain Barrat, Guilherme Ferraz de Arruda, Iacopo Iacopini, Yamir Moreno
    Pages 329-346

  15. Consensus Dynamics and Opinion Formation on Hypergraphs

    • Leonie Neuhäuser, Renaud Lambiotte, Michael T. Schaub
    Pages 347-376

  16. Collective Games on Hypergraphs

    • Unai Alvarez-Rodriguez, Federico Battiston, Guilherme Ferraz de Arruda, Yamir Moreno, Matjaž Perc, Vito Latora
    Pages 377-388

  17. Topological Data Analysis of Spatial Systems

    • Michelle Feng, Abigail Hickok, Mason A. Porter
    Pages 389-399

  18. Higher-Order Description of Brain Function

    • Paul Expert, Giovanni Petri
    Pages 401-415

  19. Higher-Order Interactions in Biology: The Curious Case of Epistasis

    • C. Brandon Ogbunugafor, Samuel V. Scarpino
    Pages 417-433
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Keywords

About this book

The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.

Editors and Affiliations

  • Department of Network and Data Science, Central European University, Vienna, Austria

    Federico Battiston

  • ISI Foundation, Turin, Italy

    Giovanni Petri

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