Generative network automata: A generalized framework for modeling adaptive network dynamics using graph rewritings

A variety of modeling frameworks have been proposed and utilized in complex systems studies, including dynamical systems models that describe state transitions on a system of fixed topology, and self-organizing network models that describe topological transformations of a network with little attention paid to dynamical state changes. Earlier network models typically assumed that topological transformations are caused by exogenous factors, such as preferential attachment of new nodes and stochastic or targeted removal of existing nodes. However, many real-world complex systems exhibit both state transition and topology transformation simultaneously, and they evolve largely autonomously based on the system's own states and topologies. Here we show that, by using the concept of graph rewriting, both state transitions and autonomous topology transformations of complex systems can be seamlessly integrated and represented in a unified computational framework. We call this novel modeling framework "Generative Network Automata (GNA)". In this chapter, we introduce basic concepts of GNA, its working definition, its generality to represent other dynamical systems models, and some of our latest results of extensive computational experiments that exhaustively swept over possible rewriting rules of simple binary-state GNA. The results revealed several distinct types of the GNA dynamics.