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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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 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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Theory of percolation on hypergraphs

Physical review. E, Journal Year: 2024, Volume and Issue: 109(1)

Published: Jan. 17, 2024

Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of bipartite network nodes hyperedges. As hypegraphs are ubiquitous, investigating hypergraph robustness is problem major research interest. In literature hypergraphs so far only has been treated adopting factor-graph percolation, which describes well remain functional even after removal one more their nodes. This approach, however, fall short to describe situations fail when any removed, this latter scenario applying, for instance, supply chains, catalytic networks, protein-interaction networks chemical reactions, etc. Here we show that these cases correct process investigate with distinct from percolation. We build message-passing theory its critical behavior using generating function formalism supported by Monte Carlo simulations on random real data. Notably, node percolation threshold exceeds graphs. Furthermore differently what happens ordinary graphs, hyperedge do not coincide, exceeding threshold. These results demonstrate fat-tailed cardinality distribution hyperedges cannot lead hyper-resilience phenomenon contrast where divergent second moment guarantees zero

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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Hypergraph reconstruction from network data

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

Published: June 15, 2021

Abstract Networks can describe the structure of a wide variety complex systems by specifying which pairs entities in system are connected. While such pairwise representations flexible, they not necessarily appropriate when fundamental interactions involve more than two at same time. Pairwise nonetheless remain ubiquitous, because higher-order often recorded explicitly network data. Here, we introduce Bayesian approach to reconstruct latent from ordinary Our method is based on principle parsimony and only includes structures there sufficient statistical evidence for them. We demonstrate its applicability range datasets, both synthetic empirical.

Language: Английский

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Inference of hyperedges and overlapping communities in hypergraphs

Nature Communications, Journal Year: 2022, Volume and Issue: 13(1)

Published: Nov. 24, 2022

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose framework based on statistical inference characterize the structural organization hypergraphs. The method allows infer missing hyperedges size in principled way, jointly detect overlapping communities presence higher-order interactions. Furthermore, our model has an efficient numerical implementation, it runs faster than dyadic algorithms pairwise records projected from data. We apply variety systems, showing strong performance hyperedge prediction tasks, detecting well aligned with information carried by interactions, robustness against addition noisy hyperedges. Our approach illustrates fundamental advantages hypergraph probabilistic when modeling relational systems

Language: Английский

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Community detection in large hypergraphs

Science Advances, Journal Year: 2023, Volume and Issue: 9(28)

Published: July 12, 2023

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. Here, we propose principled framework the organization higher-order data. Our approach recovers community structure with accuracy exceeding that currently available state-of-the-art algorithms, as tested in synthetic benchmarks both hard overlapping ground-truth partitions. is flexible allows capturing assortative disassortative structures. Moreover, our method scales orders magnitude faster than competing making it suitable for analysis very large hypergraphs, containing millions nodes thousands nodes. work constitutes practical general hypergraph analysis, broadening understanding

Language: Английский

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