Social contagion models on hypergraphs

Arruda, Guilherme Ferraz de; Petri, Giovanni; Moreno, Yamir

doi:10.1103/physrevresearch.2.023032

Cited by 181 publications

(178 citation statements)

References 36 publications

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“…In this section, we introduce and study a specific form of non-linear interaction function, aiming at modelling consensus dynamics with group reinforcement on hypergraphs. Note that other choices of non-linear interaction functions, akin to Watts threshold models [32], have been considered recently for information spreading [10]. As previously mentioned, multi-body group effects that cannot be reduced to pairwise interactions can appear in various contexts.…”

Section: A Modelling Consensus Dynamics With Group Reinforcementmentioning

confidence: 99%

“…Such systems may be represented as hypergraphs or simplicial complexes, and a substantial body of work has characterised their structural properties. However, a proper understanding of how multi-body interactions affect spreading dynamics in networked systems is still nascent [3,[8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…There are different ways of encoding the multi-body structure of a networked system. They range from set systems and general hypergraphs [10,17] to approaches adapted from algebraic topology based on simplicial complexes [9,14,[18][19][20][21][22]. Hypergraphs generalise standard networks by allowing nodes to interact through hyperedges of different sizes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multibody interactions and nonlinear consensus dynamics on networked systems

2020

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Multi-body interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyse models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multi-body dynamical effects that go beyond rescaled pairwise interactions can only appear if the interaction function is non-linear, regardless of the underlying multi-body structure. As a practical application, we introduce a specific non-linear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarised clusters where multi-body interactions make one cluster dominate the other.

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Section: A Modelling Consensus Dynamics With Group Reinforcementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multibody interactions and nonlinear consensus dynamics on networked systems

2020

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“…Once again, however, the focus is placed on lowdimensional simplicial complexes (triangles). Recently, several dynamics, including epidemic spreading [16,49,52] and synchronisation [38], have been shown to produce new collective behaviours when higher-order interactions are assumed to shape the networked arrangement. In the projected network each hyperedge Eα becomes a complete clique of size |Eα|, with thus |Eα|(|Eα| − 1)/2 pairwise interactions.…”

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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“…Networks such as these cannot be represented via the classical paradigm of dyadic graphs without loss of higher-order information. For this reason, recent scholarly attention has emphasized the role of such polyadic interactions in governing the structure and function of complex systems [5,20,12]. Polyadic data representations such as hypergraphs [7,10] and simplicial complexes [39,9] have emerged as practical modeling frameworks that directly represent interactions between arbitrary sets of agents.…”

Section: Introductionmentioning

confidence: 99%

Annotated hypergraphs: models and applications

Chodrow

Mellor

2020

Appl Netw Sci

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Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example, the order of authors on a paper often reflects the nature of their contributions to the completed work. To model these networks, we introduce annotated hypergraphs as natural polyadic generalizations of directed graphs. Annotated hypergraphs form a highly general framework for incorporating metadata into polyadic graph models. To facilitate data analysis with annotated hypergraphs, we construct a role-aware configuration null model for these structures and prove an efficient Markov Chain Monte Carlo scheme for sampling from it. We proceed to formulate several metrics and algorithms for the analysis of annotated hypergraphs. Several of these, such as assortativity and modularity, naturally generalize dyadic counterparts. Other metrics, such as local role densities, are unique to the setting of annotated hypergraphs. We illustrate our techniques on six digital social networks, and present a detailed case-study of the Enron email data set.

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Social contagion models on hypergraphs

Cited by 181 publications

References 36 publications

Multibody interactions and nonlinear consensus dynamics on networked systems

Multibody interactions and nonlinear consensus dynamics on networked systems

Random walks on hypergraphs

Annotated hypergraphs: models and applications

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