The scene graph is a novel data structure describing objects and their pairwise relationship within image scenes. As the size of scene graphs in vision and multimedia applications increases, the need for lossless storage and transmission of such data becomes more critical. However, the compression of scene graphs is less studied because of the complicated data structures involved and complex distributions. Existing solutions usually involve general-purpose compressors or graph structure compression methods, which are weak at reducing the redundancy in scene graph data. This paper introduces a novel lossless compression framework with adaptive predictors for the joint compression of objects and relations in scene graph data. The proposed framework comprises a unified prior extractor and specialized element predictors to adapt to different data elements. Furthermore, to exploit the context information within and between graph elements, Graph Context Convolution is proposed to support different graph context modeling schemes for different graph elements. Finally, an overarching framework incorporates the learned distribution model to predict numerical data under complicated conditional constraints. Experiments conducted on labeled or generated scene graphs demonstrate the effectiveness of the proposed framework for scene graph lossless compression.