  We propose a combination of a variational autoencoder and a transformer based
model which fully utilises graph convolutional and graph pooling layers to
operate directly on graphs. The transformer model implements a novel node
encoding layer, replacing the position encoding typically used in transformers,
to create a transformer with no position information that operates on graphs,
encoding adjacent node properties into the edge generation process. The
proposed model builds on graph generative work operating on graphs with edge
features, creating a model that offers improved scalability with the number of
nodes in a graph. In addition, our model is capable of learning a disentangled,
interpretable latent space that represents graph properties through a mapping
between latent variables and graph properties. In experiments we chose a
benchmark task of molecular generation, given the importance of both generated
node and edge features. Using the QM9 dataset we demonstrate that our model
performs strongly across the task of generating valid, unique and novel
molecules. Finally, we demonstrate that the model is interpretable by
generating molecules controlled by molecular properties, and we then analyse
and visualise the learned latent representation.
