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From networks to optimal higher-order models of complex systems

Nature Physics volume 15, pages 313–320 (2019)Cite this article

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  2. Integrated Science Lab, Department of Physics, Umeå University, Umeå, Sweden

    Martin Rosvall

  3. Data Analytics Group, Department of Informatics (IfI), University of Zurich, Zurich, Switzerland

    Ingo Scholtes

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  1. Renaud Lambiotte
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Correspondence to Ingo Scholtes.

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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). https://doi.org/10.1038/s41567-019-0459-y

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