  Graphs are the natural data structure to represent relational and structural
information in many domains. To cover the broad range of graph-data
applications including graph classification as well as graph generation, it is
desirable to have a general and flexible model consisting of an encoder and a
decoder that can handle graph data. Although the representative encoder-decoder
model, Transformer, shows superior performance in various tasks especially of
natural language processing, it is not immediately available for graphs due to
their non-sequential characteristics. To tackle this incompatibility, we
propose GRaph-Aware Transformer (GRAT), the first Transformer-based model which
can encode and decode whole graphs in end-to-end fashion. GRAT is featured with
a self-attention mechanism adaptive to the edge information and an
auto-regressive decoding mechanism based on the two-path approach consisting of
sub-graph encoding path and node-and-edge generation path for each decoding
step. We empirically evaluated GRAT on multiple setups including encoder-based
tasks such as molecule property predictions on QM9 datasets and
encoder-decoder-based tasks such as molecule graph generation in the organic
molecule synthesis domain. GRAT has shown very promising results including
state-of-the-art performance on 4 regression tasks in QM9 benchmark.
