Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

Nature Communications, Journal Year: 2023, Volume and Issue: 14(1)

Published: March 23, 2023

Abstract Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations such simplicial complexes hypergraphs. So far, the choice between hypergraphs has often been motivated by technical convenience. Here, using synchronization an example, we demonstrate that effects higher-order interactions are highly representation-dependent. In particular, typically enhance in but opposite effect complexes. We provide theoretical insight linking synchronizability different hypergraph structures (generalized) degree heterogeneity cross-order correlation, which turn influence wide range dynamical processes from contagion diffusion. Our findings reveal hidden impact on dynamics, highlighting importance choosing appropriate when studying with nonpairwise interactions.

Language: Английский

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Higher-order motif analysis in hypergraphs

Communications Physics, Journal Year: 2022, Volume and Issue: 5(1)

Published: April 5, 2022

Abstract A deluge of new data on real-world networks suggests that interactions among system units are not limited to pairs, but often involve a higher number nodes. To properly encode higher-order interactions, richer mathematical frameworks such as hypergraphs needed, where hyperedges describe an arbitrary Here we systematically investigate motifs, defined small connected subgraphs in which vertices may be linked by any order, and propose efficient algorithm extract complete motif profiles from empirical data. We identify different families hypergraphs, characterized distinct connectivity patterns at the local scale. also set measures study nested structure provide evidences structural reinforcement, mechanism associates strengths for nodes interact more pairwise level. Our work highlights informative power providing principled way fingerprints network microscale.

Language: Английский

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Epidemic spreading on higher-order networks

Physics Reports, Journal Year: 2024, Volume and Issue: 1056, P. 1 - 70

Published: Jan. 19, 2024

Language: Английский

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Controlling complex networks with complex nodes

Nature Reviews Physics, Journal Year: 2023, Volume and Issue: 5(4), P. 250 - 262

Published: March 24, 2023

Language: Английский

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Synchronization in multiplex networks

Physics Reports, Journal Year: 2024, Volume and Issue: 1060, P. 1 - 54

Published: Feb. 8, 2024

Language: Английский

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Collective dynamics of swarmalators with higher-order interactions

Communications Physics, Journal Year: 2024, Volume and Issue: 7(1)

Published: Feb. 21, 2024

Language: Английский

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Hyperedge overlap drives explosive transitions in systems with higher-order interactions

Nature Communications, Journal Year: 2025, Volume and Issue: 16(1)

Published: Jan. 9, 2025

Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how behavior a system is influenced by microscopic organization its interactions not fully understood. In this work, we introduce way quantify overlap among hyperedges network, and show real-world exhibit different levels intra-order hyperedge overlap. We then study two types dynamical processes on networks, namely contagion synchronization, finding plays universal role determining variety systems. Our results demonstrate alone does guarantee abrupt transitions. Rather, explosivity bistability require structure with low value Group can lead explosive onsets biological sociotechnological Here, authors it between these kind drives whether emergence synchrony epidemics shows up smoothly or abruptly.

Language: Английский

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Higher-order simplicial synchronization of coupled topological signals

Communications Physics, Journal Year: 2021, Volume and Issue: 4(1)

Published: June 7, 2021

Abstract Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from brain to social networks. Here we show that algebraic is a fundamental tool higher-order dynamics simplicial complexes. In particular consider topological signals, i.e., dynamical signals defined on simplices different dimension, here taken be nodes links for simplicity. We coupling between leads explosive synchronization in which phases synchronize simultaneously at discontinuous phase transition. study model real connectomes models. Finally, provide comprehensive theoretical approach captures this transition fully connected networks random treated within annealed approximation, establishing conditions observing closed hysteresis loop large limit.

Language: Английский

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Phase transitions and stability of dynamical processes on hypergraphs

Communications Physics, Journal Year: 2021, Volume and Issue: 4(1)

Published: Feb. 12, 2021

Abstract Hypergraphs naturally represent higher-order interactions, which persistently appear in social neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs not available yet. In this paper, we derive expressions for the stability of systems defined an arbitrary hypergraph. The allows us reveal that, near fixed point, relevant structure weighted graph-projection hypergraph that it possible identify role each structural order given process. We analytically solve two dynamics interest, namely, contagion diffusion processes, show conditions can be decoupled components. Our results process, only pairwise interactions play absorbing state, while dynamics, plays differential role. work provides further exploration hypergraphs.

Language: Английский

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Simplicial contagion in temporal higher-order networks

Journal of Physics Complexity, Journal Year: 2021, Volume and Issue: 2(3), P. 035019 - 035019

Published: July 8, 2021

Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited pairwise interactions, making it less suitable properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure multiple sources infections. Simplicial contagion has been proposed as an alternative framework simplices are used encode group interactions any order. The presence higher-order leads explosive transitions and bistability which cannot be obtained when only dyadic ties considered. In particular, critical mass effects can emerge even for infectivity values below standard threshold, size initial seed infectious nodes determines whether system would eventually fall endemic healthy state. Here we extend simplicial time-varying networks, created destroyed over time. By following microscopic Markov chain approach, find that same might not lead stationary state, depending on temporal properties underlying network structure, show persistent anticipate onset state finite-size systems. We characterize this behavior with prescribed correlation between consecutive heterogeneous complexes, showing temporality again limits effect spreading, but pronounced way than homogeneous structures. Our work suggests importance incorporating temporality, realistic feature many real-world systems, into investigation dynamical beyond interactions.

Language: Английский

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