Network Analysis of the State Space of Discrete Dynamical Systems
  We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54 and 110. We further define the \emph{path diversity} as a global network measure. The co-appearance of non-trivial scaling in both hub size and path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's Class IV and some Class III CA. 
Amer Shreim, Peter Grassberger, Walter Nadler, Bj\"orn Samuelsson,   Joshua E.S. Socolar, and Maya Paczuski