Dynamical Networks and Isospectral Graph Reductions

Abstract

This is a fundamental chapter of the book. It deals with networks, which are here considered as graphs, and is built on the theory developed in the previous chapter, on matrices. Although, the dynamical networks described in Chap. 3 are richer objects than their weighted adjacency matrices, the latter still carry the most important information about a dynamical network. Indeed, from a theoretical point of view, a network’s weighted adjacency matrix weighted adjacency matrix describes a linearization of the network’s dynamics, which in applications is often the only network information available. In fact, it is not uncommon to have only the unweighted adjacency matrix unweighted adjacency matrix of a network.