Before revision:  Here, we show that in any physically constructible geometric network, the geometry of the network  constrains and bounds signaling and the flow of information through the network , and develop a theory derived from foundational principles of neural signaling that can both describe and predict the dynamics of geometric networks from considerations of node dynamics. We provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks , specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in the visual cortex, and the internet router network, are capable of approaching a state of optimal dynamical efficiency, a concept that is derived from the theory.
After revision:  Here, we show that in any physically constructible geometric network, the geometry of the network constrains and bounds signaling and the flow of information through the network . This then in turn predicts the emergent dynamics of the network. Our results illustrate how the in- terplay between strictly local geometric and temporal process at the scale of individual node pairs directly affects the behavior of the whole network. We also provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks , specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in the visual cortex, and the internet router network, are capable of approaching a state of optimal dynamical efficiency, a concept that is derived from the theory.