Before revision:  We show how a strictly local process at the scale of individual node pairs directly affects the behavior of the system at the whole network scale. Individual nodes responding to information from the upstream nodes it is connected to produce the observable emergent dynamics of the entire networkat a global scale, independent of and without any knowledge of what all the other nodes in the network may be doing. 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.
After revision:  We show how a strictly local process at the scale of individual node pairs directly affects the behavior of the network as a whole in a deterministic way. 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 both naturally occurring and engineered networks are capable of approaching a state of optimal dynamical efficiency, one of the key results of the theory.