  Recently, there has been great success in applying deep neural networks on
graph structured data. Most work, however, focuses on either node- or
graph-level supervised learning, such as node, link or graph classification or
node-level unsupervised learning (e.g. node clustering). Despite its wide range
of possible applications, graph-level unsupervised learning has not received
much attention yet. This might be mainly attributed to the high representation
complexity of graphs, which can be represented by n! equivalent adjacency
matrices, where n is the number of nodes. In this work we address this issue by
proposing a permutation-invariant variational autoencoder for graph structured
data. Our proposed model indirectly learns to match the node ordering of input
and output graph, without imposing a particular node ordering or performing
expensive graph matching. We demonstrate the effectiveness of our proposed
model on various graph reconstruction and generation tasks and evaluate the
expressive power of extracted representations for downstream graph-level
classification and regression.
