Graph Convolutional Neural Networks and Graph Generation via Scattering

We  generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We further use it to form a graph generative model. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations and stable to signal and graph manipulations. Numerical results demonstrate competitive performance on relevant datasets for the tasks of community detection, link prediction and graph generation.