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Abrupt transition in the structural formation of interconnected networks

Nature Physics volume 9, pages 717–720 (2013)Cite this article

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Abstract

Our world is linked by a complex mesh of networks through which information, people and goods flow. These networks are interdependent on each other, and present structural and dynamical features1,2,3,4,5,6 different from those observed in isolated networks7,8,9. Although examples of such dissimilar properties are becoming more abundant—such as in diffusion, robustness and competition—it is not yet clear where these differences are rooted. Here we show that the process of building independent networks into an interconnected network of networks undergoes a structurally sharp transition as the interconnections are formed. Depending on the relative importance of inter- and intra- layer connections, we find that the entire interdependent system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act as independent entities; in the other regime, network layers are indistinguishable and the whole system behaves as a single-level network. We analytically show that the transition between the two regimes is discontinuous even for finite-size networks. Thus, any real-world interconnected system is potentially at risk of abrupt changes in its structure, which may manifest new dynamical properties.

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Figure 1: Interdependent networks.
Figure 2: First-order structural transition in interdependent networks.

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Acknowledgements

This work has been partially supported by the Spanish DGICYT Grants FIS2012-38266, FET projects PLEXMATH (318132) and the Generalitat de Catalunya 2009-SGR-838. F.R. acknowledges support from the Spanish Ministerio de Ciencia e Innovacion through the Ramón y Cajal programme. A.A. acknowledges the ICREA Academia and the James S. McDonnell Foundation.

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Authors and Affiliations

  1. Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Indiana, 47408 Bloomington, USA

    Filippo Radicchi

  2. Departament d’Enginyeria Quimica, Universitat Rovira i Virgili, 43007 Tarragona, Spain

    Filippo Radicchi

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

    Alex Arenas

  4. IPHES, Institut Catala de Paleoecologia Humana i Evoluci’o Social, 43007 Tarragona, Spain

    Alex Arenas

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  1. Filippo Radicchi
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F.R and A.A. designed and performed the research, and wrote the paper.

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Correspondence to Filippo Radicchi.

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Radicchi, F., Arenas, A. Abrupt transition in the structural formation of interconnected networks. Nature Phys 9, 717–720 (2013). https://doi.org/10.1038/nphys2761

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