  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.
