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The physics of higher-order interactions in complex systems

Abstract

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.

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Fig. 1: Pairwise and higher-order representations.
Fig. 2: Higher-order interactions lead to explosive phenomena.
Fig. 3: Higher-order systems are fully dynamical.
Fig. 4: Inference of higher-order systems is still an open and challenging problem.

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Battiston, F., Amico, E., Barrat, A. et al. The physics of higher-order interactions in complex systems. Nat. Phys. 17, 1093–1098 (2021). https://doi.org/10.1038/s41567-021-01371-4

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