  Recently much attention has been paid to the study of the robustness of
interdependent and multiplex networks and, in particular, 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)
$\alpha$ is connected with $q_{\alpha}$ randomly chosen replicas in some other
networks and is interdependent of these nodes with probability $r$. We find
that when the superdegrees $q_{\alpha}$ of different layers in the network of
networks are distributed heterogeneously, multiple percolation phase transition
can occur, and depending on the value of $r$ these transition are continuous or
discontinuous.
