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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062814. Epub 2014 Jun 26.

Multiple percolation transitions in a configuration model of a network of networks.

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School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
Departamento de Física da Universidade de Aveiro, I3N, 3810-193 Aveiro, Portugal and A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.


Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, the networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually connected component when a fraction of nodes have been removed from these networks. Here we characterize the emergence of the mutually connected component in a network of networks in which every node of a network (layer) α is connected with q_{α} its randomly chosen replicas in some other networks and is interdependent of these nodes with probability r. We find that when the superdegrees q_{α} of different layers in a network of networks are distributed heterogeneously, multiple percolation phase transition can occur. We show that, depending on the value of r, these transition are continuous or discontinuous.

[Indexed for MEDLINE]

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