On the Relation Between Non-normality and Diameter in Linear Dynamical Networks

Understanding how the “degree” of non-normality of a networked system is connected with the topological structure of the underlying graph is of crucial importance in many areas of the engineering and natural sciences, most notably in the controllability analysis of large-scale networks. This paper explores this relation in terms of the graph diam eter. More precisely, we derive diameter-dependent upper and lower bounds on network non-normality. Further, we outline a gradient-based optimization procedure to increase the nonnormality of a network.