  Graphons are general and powerful models for generating graphs of varying
size. In this paper, we propose to directly model graphons using neural
networks, obtaining Implicit Graphon Neural Representation (IGNR). Existing
work in modeling and reconstructing graphons often approximates a target
graphon by a fixed resolution piece-wise constant representation. Our IGNR has
the benefit that it can represent graphons up to arbitrary resolutions, and
enables natural and efficient generation of arbitrary sized graphs with desired
structure once the model is learned. Furthermore, we allow the input graph data
to be unaligned and have different sizes by leveraging the Gromov-Wasserstein
distance. We first demonstrate the effectiveness of our model by showing its
superior performance on a graphon learning task. We then propose an extension
of IGNR that can be incorporated into an auto-encoder framework, and
demonstrate its good performance under a more general setting of graphon
learning. We also show that our model is suitable for graph representation
learning and graph generation.
