Networks beyond pairwise interactions: Structure and dynamics

Physics Reports, Journal Year: 2020, Volume and Issue: 874, P. 1 - 92

Published: June 13, 2020

The complexity of many biological, social and technological systems stems from the richness interactions among their units. Over past decades, a great variety complex has been successfully described as networks whose interacting pairs nodes are connected by links. Yet, in face-to-face human communication, chemical reactions ecological systems, can occur groups three or more cannot be simply just terms simple dyads. Until recently, little attention devoted to higher-order architecture real systems. However, mounting body evidence is showing that taking structure these into account greatly enhance our modeling capacities help us understand predict emerging dynamical behaviors. Here, we present complete overview field beyond pairwise interactions. We first discuss methods represent give unified presentation different frameworks used describe highlighting links between existing concepts representations. review measures designed characterize models proposed literature generate synthetic structures, such random growing simplicial complexes, bipartite graphs hypergraphs. introduce rapidly research on topology. focus novel emergent phenomena characterizing landmark processes, diffusion, spreading, synchronization games, when extended elucidate relations topology properties, conclude with summary empirical applications, providing an outlook current conceptual frontiers.

Language: Английский

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The physics of higher-order interactions in complex systems

Nature Physics, Journal Year: 2021, Volume and Issue: 17(10), P. 1093 - 1098

Published: Oct. 1, 2021

Language: Английский

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Dynamics on higher-order networks: a review

Journal of The Royal Society Interface, Journal Year: 2022, Volume and Issue: 19(188)

Published: March 1, 2022

Network science has evolved into an indispensable platform for studying complex systems. But recent research identified limits of classical networks, where links connect pairs nodes, to comprehensively describe group interactions. Higher-order a link can more than two have therefore emerged as new frontier in network science. Since interactions are common social, biological and technological systems, higher-order networks recently led important discoveries across many fields research. Here, we review these works, focusing particular on the novel aspects dynamics that emerges networks. We cover variety dynamical processes thus far been studied, including different synchronization phenomena, contagion processes, evolution cooperation consensus formation. also outline open challenges promising directions future

Language: Английский

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Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching

Communications Physics, Journal Year: 2020, Volume and Issue: 3(1)

Published: Nov. 30, 2020

Synchronization processes play critical roles in the functionality of a wide range both natural and man-made systems. Recent work physics neuroscience highlights importance higher-order interactions between dynamical units, i.e., three- four-way addition to pairwise interactions, their role shaping collective behavior. Here we show that coupled phase oscillators, encoded microscopically simplicial complex, give rise added nonlinearity macroscopic system dynamics induces abrupt synchronization transitions via hysteresis bistability synchronized incoherent states. Moreover, these can stabilize strongly states even when coupling is repulsive. These findings reveal self-organized phenomenon may be responsible for rapid switching many biological other systems exhibit without need particular correlation mechanisms oscillators topological structure.

Language: Английский

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Stability of synchronization in simplicial complexes

Nature Communications, Journal Year: 2021, Volume and Issue: 12(1)

Published: Feb. 23, 2021

Abstract Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, recent studies revealed that higher-order many-body interactions are present groups, ecosystems human brain, they actually affect emergent dynamics all these systems. Here, we introduce general framework to study accounting for precise microscopic structure their at any possible order. We show complete synchronization exists an invariant solution, give necessary condition it be observed stable state. Moreover, some relevant instances, such takes form Master Stability Function. generalizes existing results valid case complex with most architecture.

Language: Английский

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The structure and dynamics of networks with higher order interactions

Physics Reports, Journal Year: 2023, Volume and Issue: 1018, P. 1 - 64

Published: May 1, 2023

Language: Английский

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What Are Higher-Order Networks?

SIAM Review, Journal Year: 2023, Volume and Issue: 65(3), P. 686 - 731

Published: Aug. 1, 2023

Network-based modeling of complex systems and data using the language graphs has become an essential topic across a range different disciplines. Arguably, this graph-based perspective derives its success from relative simplicity graphs: A graph consists nothing more than set vertices edges, describing relationships between pairs such vertices. This simple combinatorial structure makes interpretable flexible tools. The as system models, however, been scrutinized in literature recently. Specifically, it argued variety angles that there is need for higher-order networks, which go beyond paradigm pairwise relationships, encapsulated by graphs. In survey article we take stock these recent developments. Our goals are to clarify (i) what networks are, (ii) why interesting objects study, (iii) how they can be used applications.

Language: Английский

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Higher-Order Networks

Published: Nov. 23, 2021

Higher-order networks describe the many-body interactions of a large variety complex systems, ranging from brain to collaboration networks. Simplicial complexes are generalized network structures which allow us capture combinatorial properties, topology and geometry higher-order Having been used extensively in quantum gravity discrete or discretized space-time, simplicial have only recently started becoming representation choice for capturing underlying systems. This Element provides an in-depth introduction very hot topic theory, covering wide range subjects emergent hyperbolic topological data analysis dynamics. Elements aims demonstrate that provide general mathematical framework reveal how dynamics depends on geometry.

Language: Английский

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Synchronization in Hindmarsh–Rose neurons subject to higher-order interactions

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2022, Volume and Issue: 32(1)

Published: Jan. 1, 2022

Higher-order interactions might play a significant role in the collective dynamics of brain. With this motivation, we here consider simplicial complex neurons, particular, studying effects pairwise and three-body on emergence synchronization. We assume to be mediated through electrical synapses, while for second-order interactions, separately study diffusive coupling nonlinear chemical coupling. For all considered cases, derive necessary conditions synchronization by means linear stability analysis, compute errors numerically. Our research shows that even if weak strength, can lead under significantly lower first-order strengths. Moreover, overall cost is reduced due introduction compared interactions.

Language: Английский

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Temporal properties of higher-order interactions in social networks

Scientific Reports, Journal Year: 2021, Volume and Issue: 11(1)

Published: March 29, 2021

Abstract Human social interactions in local settings can be experimentally detected by recording the physical proximity and orientation of people. Such interactions, approximating face-to-face communications, effectively represented as time varying networks with links being unceasingly created destroyed over time. Traditional analyses temporal have addressed mostly pairwise where describe dyadic connections among individuals. However, many network dynamics are hardly ascribable to but often comprise larger groups, which better described higher-order interactions. Here we investigate organizations analyzing five publicly available datasets collected different settings. We find that ubiquitous and, similarly their counterparts, characterized heterogeneous dynamics, bursty trains rapidly recurring events separated long periods inactivity. evolution formation groups looking at transition rates between structures. more spontaneous settings, group slower disaggregation, while work these phenomena abrupt, possibly reflecting pre-organized dynamics. Finally, observe reinforcement suggesting longer a stays together higher probability same interaction pattern persist future. Our findings suggest importance considering structure when investigating human

Language: Английский

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