Title: Unsupervised Universal Self-Attention Network for Graph Classification. Abstract: Existing graph embedding models often have weaknesses in exploiting graph structure similarities, potential dependencies among nodes and global network properties. To this end, we present U2GAN, a novel unsupervised model leveraging on the strength of the recently introduced universal self-attention network (Dehghani et al., 2019), to learn low-dimensional embeddings of graphs which can be used for graph classification. In particular, given an input graph, U2GAN first applies a self-attention computation, which is then followed by a recurrent transition to iteratively memorize its attention on vector representations of each node and its neighbors across each iteration. Thus, U2GAN can address the weaknesses in the existing models in order to produce plausible node embeddings whose sum is the final embedding of the whole graph. Experimental results show that our unsupervised U2GAN produces new state-of-the-art performances on a range of well-known benchmark datasets for the graph classification task. It even outperforms supervised methods in most of benchmark cases.