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More is different in real-world multilayer networks

Nature Physics volume 19, pages 1247–1262 (2023)Cite this article

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An Author Correction to this article was published on 20 September 2023

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Abstract

The constituents of many complex systems are characterized by non-trivial connectivity patterns and dynamical processes that are well captured by network models. However, most systems are coupled with each other through interdependencies, characterized by relationships among heterogeneous units, or multiplexity, characterized by the coexistence of different kinds of relationships among homogeneous units. Multilayer networks provide the framework to capture the complexity typical of systems of systems, enabling the analysis of biophysical, social and human-made networks from an integrated perspective. Here I review the most important theoretical developments in the past decade, showing how the layered structure of multilayer networks is responsible for phenomena that cannot be observed from the analysis of subsystems in isolation or from their aggregation, including enhanced diffusion, emergent mesoscale organization and phase transitions. I discuss applications spanning multiple spatial scales, from the cell to the human brain and to ecological and social systems, and offer perspectives and challenges on future research directions.

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Fig. 1: Synchronization dynamics in multilayer networks.
Fig. 2: Cascade failures and percolation in multilayer networks.
Fig. 3: Coarse-graining a multilayer system.
Fig. 4: Large-scale structure of biomolecular interactions.
Fig. 5: Protein–protein interactions network.
Fig. 6: Virus-host interactions.
Fig. 7: Unfolding of empirical interdependent processes.

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Acknowledgements

M.D.D. acknowledges partial financial support from the Human Frontier Science Program Organization (HFSP ref. RGY0064/2022), from the University of Padua (PRD-BIRD 2022), from the INFN grant “LINCOLN” and from the EU funding within the MUR PNRR “National Center for HPC, BIG DATA AND QUANTUM COMPUTING” (project no. CN00000013 CN1).

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  1. Department of Physics and Astronomy “Galileo Galilei”, University of Padua, Padua, Italy

    Manlio De Domenico

  2. Padua Center for Network Medicine, University of Padua, Padua, Italy

    Manlio De Domenico

  3. Istituto Nazionale di Fisica Nucleare, Padua, Italy

    Manlio De Domenico

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De Domenico, M. More is different in real-world multilayer networks. Nat. Phys. 19, 1247–1262 (2023). https://doi.org/10.1038/s41567-023-02132-1

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