In this paper, we study the problem of parsing structured knowledge graphs from textual descriptions. In particular, we consider the scene graph representation that considers objects together with their attributes and relations: this representation has been proved useful across a variety of vision and language applications. We begin by introducing an alternative but equivalent edge-centric view of scene graphs that connect to dependency parses. Together with a careful redesign of label and action space, we combine the two-stage pipeline used in prior work (generic dependency parsing followed by simple post-processing) into one, enabling end-to-end training. The scene graphs generated by our learned neural dependency parser achieve an F-score similarity of 49.67% to ground truth graphs on our evaluation set, surpassing best previous approaches by 5%. We further demonstrate the effectiveness of our learned parser on image retrieval applications.