Mutually connected component of network of networks with replica nodes

Abstract

We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove that if in these networks, all the nodes of one network (layer) are interdependent on the nodes of the same other interconnected layer, then, remarkably, the mutually connected component does not depend on the topology of the network of networks. This component coincides with the mutual component of the fully connected network of networks constructed from the same set of layers, i.e., a multiplex network.

(9 pages, 2 figures )

References in corpus (5)

• The structure and dynamics of multilayer networks
• Critical phenomena in complex networks
• Diffusion dynamics on multiplex networks
• Percolation on sparse networks
• Multiple percolation transitions in a configuration model of network of networks

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• Efficient algorithm to compute mutually connected components in interdependent networks
• Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review
• Majority-vote dynamics on multiplex networks
• Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions
• Percolation of Hierarchical Networks and Networks of Networks
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