Effective decoding in graph auto-encoder using triadic closure

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.