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

Nature Communications, Год журнала: 2023, Номер 14(1)

Опубликована: Март 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.

Язык: Английский

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Epidemic spreading on higher-order networks

Physics Reports, Год журнала: 2024, Номер 1056, С. 1 - 70

Опубликована: Янв. 19, 2024

Язык: Английский

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Synchronization induced by directed higher-order interactions

Communications Physics, Год журнала: 2022, Номер 5(1)

Опубликована: Окт. 28, 2022

Abstract Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for networks with pairwise interactions, its effects systems higher-order have not yet explored as deserved. Here, we introduce the concept of M -directed hypergraphs, general class directed structures, which allows to investigate dynamical coupled through group interactions. As an application study synchronization nonlinear oscillators on 1-directed finding that can destroy synchronization, but also stabilize otherwise unstable synchronized states.

Язык: Английский

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Weighted simplicial complexes and their representation power of higher-order network data and topology

Physical review. E, Год журнала: 2022, Номер 106(3)

Опубликована: Сен. 26, 2022

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from collaboration networks to brain networks. One open problem in field is what should drive choice adopted mathematical framework describe starting data interactions. Unweighted simplicial typically involve a loss information data, though having benefit topology data. In this work we show that weighted allow circumvent all limitations unweighted represent particular, can without information, allowing at same time The probed by studying spectral properties suitably defined Hodge Laplacians displaying normalized spectrum. spectrum (weighted) here studied combining cohomology theory with theory. proposed framework, quantify compare content spectra different dimension using entropies relative entropies. methodology tested on real version model "Network Geometry Flavor".

Язык: Английский

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Diffusion-driven instability of topological signals coupled by the Dirac operator

Physical review. E, Год журнала: 2022, Номер 106(6)

Опубликована: Дек. 23, 2022

The study of reaction-diffusion systems on networks is paramount relevance for the understanding nonlinear processes in where topology intrinsically discrete, such as brain. Until now, have been studied only when species are defined nodes a network. However, number real including, e.g., brain and climate, dynamical variables not but also links, faces, higher-dimensional cells simplicial or cell complexes, leading to topological signals. In this work, we signals coupled through Dirac operator. operator allows different dimension interact cross-diffuse it projects simplices given one up down. By focusing framework involving establish conditions emergence Turing patterns show that latter never localized links Moreover, display pattern their projection does well. We validate theory hereby developed benchmark network model square lattices with periodic boundary conditions.

Язык: Английский

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Global topological synchronization of weighted simplicial complexes

Physical review. E, Год журнала: 2024, Номер 110(1)

Опубликована: Июль 31, 2024

Higher-order networks are able to capture the many-body interactions present in complex systems and unveil fundamental phenomena revealing rich interplay between topology, geometry, dynamics. Simplicial complexes higher-order that encode topology dynamics of systems. Specifically, simplicial can sustain topological signals, i.e., dynamical variables not only defined on nodes network but also their edges, triangles, so on. Topological signals undergo collective such as synchronization, however, some topologies global synchronization signals. Here we consider weighted complexes. We demonstrate globally synchronize complexes, even if they odd-dimensional, e.g., edge thus overcoming a limitation unweighted case. These results more advantageous for observing these than counterpart. In particular, two complexes: triangulated torus waffle. completely characterize spectral properties that, under suitable conditions weights, Our interpreted geometrically by showing, among other results, cases weights be associated with lengths sides curved simplices.

Язык: Английский

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Ranking cliques in higher-order complex networks

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2023, Номер 33(7)

Опубликована: Июль 1, 2023

Traditional network analysis focuses on the representation of complex systems with only pairwise interactions between nodes. However, higher-order structure, which is beyond interactions, has a great influence both dynamics and function. Ranking cliques could help understand more emergent dynamical phenomena in large-scale networks structures, regarding important issues, such as behavioral synchronization, evolution, epidemic spreading. In this paper, motivated by multi-node topological simplex, several centralities are proposed, namely, cycle (HOC) ratio, degree, H-index, PageRank (HOP), to quantify rank importance cliques. Experiments synthetic real-world support that, compared other traditional metrics, proposed effectively reduce dimension accurate finding set vital Moreover, since critical ranked HOP HOC scattered over network, outperform metrics ranking that maintaining connectivity, thereby facilitating synchronization virus spread control applications.

Язык: Английский

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Measuring the significance of higher-order dependency in networks

New Journal of Physics, Год журнала: 2024, Номер 26(3), С. 033032 - 033032

Опубликована: Фев. 27, 2024

Abstract Higher-order networks (HONs), which go beyond the limitations of pairwise relation modeling by graphs, capture higher-order dependencies involving three or more components for various systems. As number potential increases exponentially with both network size and order dependency, it is particular importance HON models to balance their representation power against model complexity. In this study, we propose a method, significant k -order mining (S DM), based on hypothesis testing Markov chain Monte Carlo (MCMC), identify in real Through synthetic clickstreams elaborately designed dependencies, S DM shows powerful ability correctly all at preset significance levels α = {0} {.01, 0} {.05, {.10} , performing as only comparison state arts, that can robustly maintain Type I error rate, without generating any II across experimental settings. We further apply method empirical networks, including journal citations, air traffic, email communications. Empirical results show among those tested 6.03%, 1.47%, 1.28% are statistical ( \textrm{{0}}\textrm{{.01}}$?> {.01} ). The proposed therefore, provides an efficient tool analysis tasks reduced computational

Язык: Английский

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Turing patterns on discrete topologies: from networks to higher-order structures

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, Год журнала: 2024, Номер 480(2302)

Опубликована: Ноя. 1, 2024

Nature is a blossoming of regular structures, signature self-organization the underlying microscopic interacting agents. Turing theory pattern formation one most studied mechanisms to address such phenomena and has been applied widespread gallery disciplines. himself used spatial discretization hosting support eventually deal with set ODEs. Such an idea contained seeds on discrete support, which fully acknowledged birth network science in early 2000s. This approach allows us tackle several settings not displaying trivial continuous embedding, as multiplex, temporal networks and, recently, higher-order structures. line research mostly confined within community, despite its inherent potential transcend conventional boundaries PDE-based patterns. Moreover, topology for novel dynamics be generated via universal formalism that can readily extended account The interplay between pave way further developments field.

Язык: Английский

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Rhythmic dynamics of higher-order phase oscillator populations with competitive couplings

Nonlinear Dynamics, Год журнала: 2024, Номер unknown

Опубликована: Окт. 3, 2024

Язык: Английский

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