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The physics of spreading processes in multilayer networks

Nature Physics volume 12, pages 901–906 (2016)Cite this article

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Abstract

Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.

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Figure 1: Multilayer networks.
Figure 2: Dynamical processes on multilayer networks.
Figure 3: Single dynamics on a multilayer network.
Figure 4: Coupled dynamics on multilayer networks.

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Change history

  • 23 February 2018

    In the version of this Progress Article originally published, the left and right panels of Fig. 3, clarifying the details indicated within the centre panel, were mistakenly interchanged. This has now been corrected in all versions of the Progress Article.

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Acknowledgements

All authors were funded by FET-Proactive project PLEXMATH (FP7-ICT-2011-8; grant #317614) funded by the European Commission. M.D.D. acknowledges financial support from the Spanish programme Juan de la Cierva (IJCI-2014–20225). C.G. acknowledges financial support from a James S. McDonnell Foundation postdoctoral fellowship. A.A. acknowledges financial support from the ICREA Academia, the James S. McDonnell Foundation, and FIS2015–38266. M.A.P. acknowledges a grant (EP/J001759/1) from the EPSRC. The authors acknowledge help from S. Agnello on the creative design of figures.

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Authors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain

    Manlio De Domenico & Alex Arenas

  2. Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599–3250, USA

    Clara Granell

  3. Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

    Mason A. Porter

  4. CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK

    Mason A. Porter

  5. Department of Mathematics, University of California, Los Angeles, California 90095, USA

    Mason A. Porter

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  1. Manlio De Domenico
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De Domenico, M., Granell, C., Porter, M. et al. The physics of spreading processes in multilayer networks. Nature Phys 12, 901–906 (2016). https://doi.org/10.1038/nphys3865

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