Multibody interactions and nonlinear consensus dynamics on networked systems

Neuhäuser, Leonie; Mellor, Andrew; Lambiotte, Renaud

doi:10.1103/physreve.101.032310

Cited by 119 publications

(102 citation statements)

References 43 publications

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“…Interestingly, more complicated nonlinear dynamics have been also recently studied on simplicial complexes [16,20,49,50] or in a pure multi-body frame [51]. Once again, however, the focus is placed on lowdimensional simplicial complexes (triangles).…”

Section: Introductionmentioning

confidence: 99%

Random walks on hypergraphs

Battiston²,

et al. 2020

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In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but involve larger sets of nodes, at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. We hereby propose a new class of random walks defined on such higher-order structures, and grounded on a microscopic physical model where multi-body proximity is associated to highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterisation of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalised random walk Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have a full control of the high-order structures, and real-world networks where higher-order interactions are at play. As a first application of the method, we compare the behaviour of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As a second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unveiling the effect of higher-order interactions on diffusive processes in higher-order networks, shading light on mechanisms at the hearth of biased information spreading in complex networked systems.

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Section: Introductionmentioning

confidence: 99%

Random walks on hypergraphs

Battiston²,

et al. 2020

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“…We hereby focus on hypergraphs [8,17,23], versatile tools with a broad potential that is still being fully elucidated. Hypergraphs have been applied to different fields from social contagion model [15,20], to the modelling of random walks [11], from the study of synchronisation [28,35,12] and diffusion [20], to non-linear consensus [37], via the emergence of Turing patterns [12]. It is also worth mentioning an alternative approach to high-order interactions which exploits the notion of simplicial complexes [16,14,41].…”

Section: Introductionmentioning

confidence: 99%

Dynamical systems on hypergraphs

2020

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We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resulting from the many-body interaction between fundamental units. In particular we will focus, on two relevant settings. First, we will assume long-ranged mean field interactions between populations, and then turn to considering diffusive-like couplings. Two applications are presented, respectively to a generalised Volterra system and the Brusselator model.

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“…We also showcased its use as reference models in investigating epidemic spreading and evolution of cooperation on hypergraphs. Models of dynamical processes on hypergraphs, such as the epidemic spreading [59]- [61], [63], evolutionary dynamics [48], [64], opinion dynamics [65]- [67], and synchronization [68]- [71], have been proposed. Deploying the hyper dK-series to studies of various models of dynamics is expected to better reveal how the dynamics depend on the specific structural properties of the given hypergraphs.…”

Section: Discussionmentioning

confidence: 99%

Randomizing Hypergraphs Preserving Degree Correlation and Local Clustering

Nakajima

Shudo

Masuda

2022

IEEE Trans. Netw. Sci. Eng.

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Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dK -series, by extending the socalled dK -series for dyadic networks to the case of hypergraphs. The hyper dK -series preserves up to the individual node's degree, node's degree correlation, node's redundancy coefficient, and/or the hyperedge's size depending on the parameter values. Furthermore, we numerically find that higher-order hyper dKseries more accurately preserves the shortest path length and degree distribution of the one-mode projection of the original hypergraph, which the method does not intend to preserve. We also apply the hyper dK -series to numerical simulations of epidemic spreading and evolutionary game dynamics on empirical social hypergraphs. We find that the hyperedge's size affects these dynamics more than any of the node's properties and that the node's degree correlation and redundancy in the empirical hypergraphs promote cooperation.

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Multibody interactions and nonlinear consensus dynamics on networked systems

Cited by 119 publications

References 43 publications

Random walks on hypergraphs

Random walks on hypergraphs

Dynamical systems on hypergraphs

Randomizing Hypergraphs Preserving Degree Correlation and Local Clustering

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