  We present an intuitive formalism for implementing cellular automata on
arbitrary topologies. By that means, we identify a symmetry operation in the
class of elementary cellular automata. Moreover, we determine the subset of
topologically sensitive elementary cellular automata and find that the overall
number of complex patterns decreases under increasing neighborhood size in
regular graphs. As exemplary applications, we apply the formalism to complex
networks and compare the potential of scale-free graphs and metabolic networks
to generate complex dynamics.
