Network automata: Coupling structure and function in dynamic networks

We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. To demonstrate its implementation we describe a simple model which exhibits behavior similar to the "Game of Life" before recasting some simple, wellknown network models as Network Automata. We then introduce Functional Network Automata which are useful for dealing with networks in which the topology evolves according to some specified microscopic rules and, simultaneously, there is a dynamic process taking place on the network that both depends on its structure but is also capable of modifying it. It is a generic framework for modeling systems in which network structure, dynamics, and function are interrelated. At the practical level, this framework allows for precise, unambiguous implementation of the microscopic rules involved in such systems. To demonstrate the approach, we develop a family of simple biologically inspired models of fungal growth.