  Cellular automata (CA) are a class of computational models that exhibit rich
dynamics emerging from the local interaction of cells arranged in a regular
lattice. In this work we focus on a generalised version of typical CA, called
graph cellular automata (GCA), in which the lattice structure is replaced by an
arbitrary graph. In particular, we extend previous work that used convolutional
neural networks to learn the transition rule of conventional CA and we use
graph neural networks to learn a variety of transition rules for GCA. First, we
present a general-purpose architecture for learning GCA, and we show that it
can represent any arbitrary GCA with finite and discrete state space. Then, we
test our approach on three different tasks: 1) learning the transition rule of
a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of
flocking agents; 3) learning a rule that converges to a desired target state.
