In this work, we addresses the problem of modeling distributions of graphs.
We introduce the Vector-Quantized Graph Auto-Encoder (VQ-GAE), a
permutation-equivariant discrete auto-encoder and designed to model the
distribution of graphs. By exploiting the permutation-equivariance of graph
neural networks (GNNs), our autoencoder circumvents the problem of the ordering
of the graph representation. We leverage the capability of GNNs to capture
local structures of graphs while employing vector-quantization to prevent the
mapping of discrete objects to a continuous latent space. Furthermore, the use
of autoregressive models enables us to capture the global structure of graphs
via the latent representation. We evaluate our model on standard datasets used
for graph generation and observe that it achieves excellent performance on some
of the most salient evaluation metrics compared to the state-of-the-art