Scene graph representations, which form a graph of visual object nodes together with their attributes and relations, have proved useful across a variety of vision and language applications. Recent work in the area has used Natural Language Processing dependency tree methods to automatically build scene graphs. In this work, we present an 'Attention Graph' mechanism that can be trained endto-end, and produces a scene graph structure that can be lifted directly from the top layer of a standard Transformer model. The scene graphs generated by our model achieve an F-score similarity of 52.21% to ground-truth graphs on the evaluation set using the SPICE metric, surpassing the best previous approaches by 2.5%.