Networks beyond pairwise interactions: Structure and dynamics

Battiston, Federico; Cencetti, Giulia; Iacopini, Iacopo; Latora, Vito; Lucas, Maxime; Patania, Alice; Young, Jean-Gabriel; Petri, Giovanni

doi:10.1016/j.physrep.2020.05.004

Cited by 1,079 publications

(832 citation statements)

References 609 publications

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“…Most interacting systems have so far been represented as networks, a collection of nodes and links describing relationships and influences between them at the level of pairs. However, many real-world systems are better modeled by including higher-order interactions, i.e., interactions between more than two nodes at a time [11]. A typical example is that of human collaborations, which often occur at the level of groups.…”

Section: Introductionmentioning

confidence: 99%

Multiorder Laplacian for synchronization in higher-order networks

Lucas

Cencetti

Battiston³

2020

Phys. Rev. Research

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136

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The emergence of synchronization in systems of coupled agents is a pivotal phenomenon in physics, biology, computer science, and neuroscience. Traditionally, interaction systems have been described as networks, where links encode information only on the pairwise influences among the nodes. Yet, in many systems, interactions among the units take place in larger groups. Recent work has shown that the presence of higher-order interactions between oscillators can significantly affect the emerging dynamics. However, these early studies have mostly considered interactions up to four oscillators at time, and analytical treatments are limited to the all-to-all setting. Here, we propose a general framework that allows us to effectively study populations of oscillators where higher-order interactions of all possible orders are considered, for any complex topology described by arbitrary hypergraphs, and for general coupling functions. To this end, we introduce a multiorder Laplacian whose spectrum determines the stability of the synchronized solution. Our framework is validated on three structures of interactions of increasing complexity. First, we study a population with all-to-all interactions at all orders, for which we can derive in a full analytical manner the Lyapunov exponents of the system, and for which we investigate the effect of including attractive and repulsive interactions. Second, we apply the multiorder Laplacian framework to synchronization on a synthetic model with heterogeneous higher-order interactions. Finally, we compare the dynamics of coupled oscillators with higher-order and pairwise couplings only, for a real dataset describing the macaque brain connectome, highlighting the importance of faithfully representing the complexity of interactions in real-world systems. Taken together, our multiorder Laplacian allows us to obtain a complete analytical characterization of the stability of synchrony in arbitrary higher-order networks, paving the way toward a general treatment of dynamical processes beyond pairwise interactions.

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Section: Introductionmentioning

confidence: 99%

Multiorder Laplacian for synchronization in higher-order networks

Lucas

Cencetti

Battiston³

2020

Phys. Rev. Research

Self Cite

136

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“…PH has also been applied to larger-scale biological systems, including leaf-venation patterns [40], aggregation models [41], human migration [42], networks of blood vessels [43], and the effects of psychoactive substances on brain activity [44]. The recent review article [45] includes an extensive discussion of applications of PH to networks.…”

Section: Introductionmentioning

confidence: 99%

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Feng

Porter

2020

Phys. Rev. Research

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Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks-including both synthetic and natural ones-using topological methods that we developed recently for analyzing spatial systems. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs that were spun by spiders under the influence of various psychotropic substances.

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“…In practice, this task is difficult because network estimation methods differ in their preference for sparsity, which affects the estimated degree distribution. Better data generation follows from more studies examining and reporting the topology of psychological networks (e.g., Battiston et al, 2020), which can in turn be used to train better neural networks to make more valid predictions.…”

Section: Discussionmentioning

confidence: 99%

Factor or Network Model? Predictions From Neural Networks

Christensen¹,

Golino²

2020

Preprint

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The nature of associations between variables is important for constructing theory about psychological phenomena. In the last decade, this topic has received renewed interested with the introduction of psychometric network models. In psychology, these models are often contrasted with latent variable (e.g., factor) models. Recent research has shown that the differences between the two tend to be more substantive than statistical (i.e., equivalent statistical representations but differing data generating hypotheses). Still, some researchers have shown that there may exist differences when data are generated from these models (e.g., sparse network models and unidimensional factor models). One recently developed algorithm called the Loadings Comparison Test (LCT) takes advantage of the loading structures of network and factor models to predict whether data were generated from a random, factor, or network model. A significant limitation in the current implementation of the LCT is that it’s based on heuristics that were derived from descriptive statistics of a limited set of data structures. In the present study, we used artificial neural networks to replace these heuristics, and develop a more robust and generalizable algorithm. We performed a simulation study that compared neural networks to the original LCT algorithm as well as logistic regression models that were trained on the same data. We found that the neural networks performed as well as or better than both methods, demonstrating generalizablity across data generating models. We echo the call for more formal theories about the relations between variables and discuss the role of the LCT in this process.

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Networks beyond pairwise interactions: Structure and dynamics

Cited by 1,079 publications

References 609 publications

Multiorder Laplacian for synchronization in higher-order networks

Multiorder Laplacian for synchronization in higher-order networks

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Factor or Network Model? Predictions From Neural Networks

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