  We study the effect of topology variation on the dynamic behavior of a system
with local update rules. We implement one-dimensional binary cellular automata
on graphs with various topologies by formulating two sets of degree-dependent
rules, each containing a single parameter. We observe that changes in graph
topology induce transitions between different dynamic domains (Wolfram classes)
without a formal change in the update rule. Along with topological variations,
we study the pattern formation capacities of regular, random, small-world and
scale-free graphs. Pattern formation capacity is quantified in terms of two
entropy measures, which for standard cellular automata allow a qualitative
distinction between the four Wolfram classes. A mean-field model explains the
dynamic behavior of random graphs. Implications for our understanding of
information transport through complex, network-based systems are discussed.
