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From networks to optimal higher-order models of complex systems


Rich data are revealing that complex dependencies between the nodes of a network may not be captured by models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

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Fig. 1: Different approaches to model an ego network with higher-order dependencies between nodes.
Fig. 2: Non-Markovian higher-order models can better capture the topology of paths in complex systems.
Fig. 3: Community detection of paths can capture overlapping communities.
Fig. 4: Non-Markovian paths change the centrality of nodes in time-stamped social network data.
Fig. 5: De Bruijn graphs with m dimensions help generalize network analytic methods to higher-order models.
Fig. 6: Non-Markovian paths in networked systems influence the evolution of diffusion processes.


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M.R. was supported by the Swedish Research Council, grant 2016-00796. I.S. acknowledges support by the Swiss National Science Foundation, grant 176938.

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Correspondence to Ingo Scholtes.

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Journal peer review information: Nature Physics thanks David Gleich and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Lambiotte, R., Rosvall, M. & Scholtes, I. From networks to optimal higher-order models of complex systems. Nat. Phys. 15, 313–320 (2019).

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