© 2019 by the authors. In realizing the network environment assumed by the Internet-of-Things, network slicing has drawn considerable attention as a way to enhance the utilization of physical networks (PNs). Meanwhile, slicing has been shown to cause interdependence among sliced virtual networks (VNs) by propagating traffic fluctuations from one network to others. However, for interconnected networks with mutual dependencies, known as a network of networks (NoN), finding a reliable design method that can cope with environmental changes is an important issue that is yet to be addressed. Some NoN models exist that describe the behavior of interdependent networks in complex systems, and previous studies have shown that an NoN model based on the functional networks of the brain can achieve high robustness, but its application to dynamic and practical systems is yet to be considered. Consequently, this paper proposes the Physical-Virtual NoN (PV-NoN) model assuming a network-slicing environment. This model defines an NoN availability state to deal with traffic fluctuations and interdependence among a PN and VNs. Further, we assume three basic types of interdependence among VNs for this model. Simulation experiments confirm that the one applying complementary interdependence inspired by brain functional networks achieves high availability and communication performance while preventing interference among the VNs. Also investigated is a method for designing a reliable network structure for the PV-NoN model. To this end, the deployment of network influencers (i.e., the most influential elements over the entire network) is configured from the perspective of intra/internetwork assortativity. Simulation experiments confirm that availability or communication performance is improved when each VN is formed assortatively or disassortatively, respectively. Regarding internetwork assortativity, both the availability and communication performance are improved when the influencers are deployed disassortatively among the VNs.