Generalized Graph Product: Spectrum, Trajectories and Controllability

Abstract

This paper presents a collection of properties on composite networks in terms of the properties on their respective factor networks. We explore a large class of composite networks using the notion of a generalized graph product. We provide the spectral properties as well as the trajectory of linear networked dynamics systems driven by the composite network's adjacency matrix. This work extends our previous research on controllability of the networked system via Cartesian product [1] to a broader family of graph products.