Networks beyond pairwise interactions: structure and dynamics

By Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, Giovanni Petri. Physics reports, 2020

1,652 citations recorded by the source corpus.

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads. Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions. We first discuss the methods to represent higher-order interactions and give a unified presentation of the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures, such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. We focus on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond pairwise interactions. We elucidate the relations between higher-order topology and dynamical properties, and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6c2f04066d9e6cf39b720b05dfc87900d3854227

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

What are higher-order networks? (2021, background): “For a more comprehensive recent review the interested reader may consult the surveys by Kahle, and Bobrowski and Kahle [39,157] (see also [23]).”
Dynamics on higher-order networks: a review (2022, background): “However, for a complete explanation of many complex systems, one needs to further improve the structural modelling of networked systems [8,9].”
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (2021, background): “Among many modelling frameworks that have been proposed to describe complex systems with higherorder relations (Battiston et al., 2020), we specifically focus on simplicial complexes, a convenient middle ground between graphs (which are a particular case of simplicial ar X iv :2 10 3.”