Non-normality Improves Information Transmission Performance of Network Systems

 In this article, we propose a new measure of communication performance of linear network systems, the information gain, and we show that this measure is strongly affected by the degree of non-normality of the network's adjacency matrix. Specifically, we prove that the numerical abscissa of the network's adjacency matrix, a well-known indicator of matrix non-normality, regulates the behavior of the information gain. Furthermore, we establish a lower bound on the information gain of positive networks, i.e., weighted networks with positive weights. This bound reveals that the information gain may exhibit an exponential dependence on the graphical distance between the transmitter and the receiver nodes. Finally, we present a design methodology that provably enhances the information gain while keeping the network's weights bounded in magnitude. We illustrate and validate our theoretical findings by means of examples with structured and random networks.