  Graphon is a nonparametric model that generates graphs with arbitrary sizes
and can be induced from graphs easily. Based on this model, we propose a novel
algorithmic framework called \textit{graphon autoencoder} to build an
interpretable and scalable graph generative model. This framework treats
observed graphs as induced graphons in functional space and derives their
latent representations by an encoder that aggregates Chebshev graphon filters.
A linear graphon factorization model works as a decoder, leveraging the latent
representations to reconstruct the induced graphons (and the corresponding
observed graphs). We develop an efficient learning algorithm to learn the
encoder and the decoder, minimizing the Wasserstein distance between the model
and data distributions. This algorithm takes the KL divergence of the graph
distributions conditioned on different graphons as the underlying distance and
leads to a reward-augmented maximum likelihood estimation. The graphon
autoencoder provides a new paradigm to represent and generate graphs, which has
good generalizability and transferability.
