  We introduce space-time graph neural network (ST-GNN), a novel GNN
architecture, tailored to jointly process the underlying space-time topology of
time-varying network data. The cornerstone of our proposed architecture is the
composition of time and graph convolutional filters followed by pointwise
nonlinear activation functions. We introduce a generic definition of
convolution operators that mimic the diffusion process of signals over its
underlying support. On top of this definition, we propose space-time graph
convolutions that are built upon a composition of time and graph shift
operators. We prove that ST-GNNs with multivariate integral Lipschitz filters
are stable to small perturbations in the underlying graphs as well as small
perturbations in the time domain caused by time warping. Our analysis shows
that small variations in the network topology and time evolution of a system
does not significantly affect the performance of ST-GNNs. Numerical experiments
with decentralized control systems showcase the effectiveness and stability of
the proposed ST-GNNs.
