  The (variational) graph auto-encoder and its variants have been popularly
used for representation learning on graph-structured data. While the encoder is
often a powerful graph convolutional network, the decoder reconstructs the
graph structure by only considering two nodes at a time, thus ignoring possible
interactions among edges. On the other hand, structured prediction, which
considers the whole graph simultaneously, is computationally expensive. In this
paper, we utilize the well-known triadic closure property which is exhibited in
many real-world networks. We propose the triad decoder, which considers and
predicts the three edges involved in a local triad together. The triad decoder
can be readily used in any graph-based auto-encoder. In particular, we
incorporate this to the (variational) graph auto-encoder. Experiments on link
prediction, node clustering and graph generation show that the use of triads
leads to more accurate prediction, clustering and better preservation of the
graph characteristics.
