Algebraic Connectivity Invariance of Network-of-Networks Derived from a Graph Product

This paper presents algebraic connectivity invariance of a network-of-networks derived from a graph product. The network is modeled as an interconnected system of several kinds of similar subsystems via a certain structure, where several vertices of each subsystem are attached to the structure. The algebraic connectivity of this network can be characterized by using an appropriate network having homogeneous subsystems under a certain condition, which is investigated in this paper. In particular, a necessary and sufficient condition for adding links (edges) to subsystems which preserve the algebraic connectivity is clarified.