Before revision: The functional and computational power of a network emerges as a prop- erty of the system operating as a coherent whole at a global scale, not at the scale of individual nodes. A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such away that they produce emergent global network dynamics? Here, we address this question by developing a generalized theoretical framework that formally describes how in any physically constructible geometric network, the geome- try of the network i.e. its physical structure, constrains and bounds signaling and the flow of information through the network.
After revision: Understanding how local interactions among connected nodes in a network result in global network dynamics and behaviors remains a critical open problem in network theory. This is important both for understanding complex networks, including the brain, and for the controlled design of networks intended to achieve a specific function. Here, we describe the construction and theoretical analysis of a framework derived from canonical neurophysiological principles that models the competing dynamics of incident signals into nodes along directed edges in a network. The framework describes the dynamics between the offset in the latencies of propagating signals, which reflect the geometry of the edges and conduction velocities, and the geome- try of the network i.e. its physical structure, constrains and bounds signaling and the flow of information through the network.