Collective dynamics on higher-order networks

Federico Battiston; Christian Bick; Maxime Lucas; Ana P. Millán; Per Sebastian Skardal; Yuanzhao Zhang

doi:10.1038/s42254-025-00916-3

Collective dynamics on higher-order networks

Federico Battiston^*
, Christian Bick^*
, Maxime Lucas^*
, Ana P. Millán
, Per Sebastian Skardal
, Yuanzhao Zhang^*

^*Corresponding author for this work

Department of Network and Data Science

Libera Universita Internazionale degli Studi Sociali Guido Carli
Vrije Universiteit Amsterdam
Technical University of Munich
University of Exeter
University of Oxford
Universite de Namur
Université catholique de Louvain
University of Granada
Trinity College Hartford
Santa Fe Institute

Research output: Contribution to journal › Review Article › peer-review

Abstract (may include machine translation)

Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here, we provide an overview of this rapidly growing field and of the techniques that can be used to describe and analyse them. We focus in particular on new phenomena and challenges that emerge when non-pairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-order networks.

Original language	English
Pages (from-to)	146-159
Number of pages	14
Journal	Nature Reviews Physics
Volume	8
Issue number	3
DOIs	https://doi.org/10.1038/s42254-025-00916-3
State	Published - Mar 2026

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10.1038/s42254-025-00916-3

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title = "Collective dynamics on higher-order networks",

abstract = "Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here, we provide an overview of this rapidly growing field and of the techniques that can be used to describe and analyse them. We focus in particular on new phenomena and challenges that emerge when non-pairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-order networks.",

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AU - Battiston, Federico

AU - Bick, Christian

AU - Lucas, Maxime

AU - Millán, Ana P.

AU - Skardal, Per Sebastian

AU - Zhang, Yuanzhao

PY - 2026/3

Y1 - 2026/3

N2 - Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here, we provide an overview of this rapidly growing field and of the techniques that can be used to describe and analyse them. We focus in particular on new phenomena and challenges that emerge when non-pairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-order networks.

AB - Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here, we provide an overview of this rapidly growing field and of the techniques that can be used to describe and analyse them. We focus in particular on new phenomena and challenges that emerge when non-pairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-order networks.

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U2 - 10.1038/s42254-025-00916-3

DO - 10.1038/s42254-025-00916-3

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JO - Nature Reviews Physics

JF - Nature Reviews Physics

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Collective dynamics on higher-order networks

Abstract (may include machine translation)

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