Before revision:  We then provide empirical evidence that at least some important examples of both naturally occurring and engineered networks are capable of approaching a state of optimal dynamical efficiency, one of the key results of the theory. While we progressively build up to what this formally means, informally it means that these networks have evolved or have been designed to optimize how they are able to handle the processing of information by matching the dynamical requirements of individual nodes to the flow of information (i.e. signals) between nodes in the network . In different ways, we use the theory to investigate properties of pyramidal neurons in biological neural networks in the visual cortex, the prevalence of the small world network topology, and the internet router network  .
After revision:  We then provide empirical evidence that at least some important examples of both naturally occurring and engineered networks , specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in biological neural networks in the visual cortex, the prevalence of the small world network topology, and the internet router network .