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The physics of higher-order interactions in complex systems


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).

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