Before revision: In any physically constructible network there is a structure-function relationship between the geometry of the network and its dynamics. The network's geometry, i.e. its physical structure, constrains and bounds signaling and the flow of information through the network. In this paper we explore how the physical geometry of a network constrains and ultimately determines its dynamics. We construct a formal theoretical framework of the relationship between network structure and function and how information flows through a network. 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.
After revision: The functional and computational power of a network emerges as a property 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 a way that they produce emergent global network dynamics? There is in general a lack of sufficient theory capable of providing insights into universal physical principles that bridge individual node dynamics to the behavior of the system at the whole network scale.