Network representation of cellular automata

Abstract

Cellular automata have been used for modeling numerous complex processes and network theory provides powerful techniques for studying the structural properties of complex systems. In this article, we present a network representation of one-dimensional binary cellular automata and investigate their dynamical properties using the structural parameters of network theory. Specifically, networks derived from the independent rules of elementary cellular automata and 5-neighbor totalistic cellular automata are investigated. We found that the network parameters, efficiency, cluster coefficients, and degree distributions are all useful in classifying and characterizing cellular automata and that certain rules of the 5-neighbor totalistic cellular automata have networks of a scale-free nature.