Abstract
We describe a giant mutually connected component in a wide class of networks
of networks. 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 graph.
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