Salient object ranking (SOR) aims to segment salient objects in an image and simultaneously predict their saliency rankings, according to the shifted human attention over different objects. The existing SOR approaches mainly focus on object-based attention, e.g., the semantic and appearance of object. However, we find that the scene context plays a vital role in SOR, in which the saliency ranking of the same object varies a lot at different scenes. In this paper, we thus make the first attempt towards explicitly learning scene context for SOR. Specifically, we establish a large-scale SOR dataset of 24,373 images with rich context annotations, i.e., scene graphs, segmentation, and saliency rankings. Inspired by the data analysis on our dataset, we propose a novel graph hypernetwork, named HyperSOR, for context-aware SOR. In HyperSOR, an initial graph module is developed to segment objects and construct an initial graph by considering both geometry and semantic information. Then, a scene graph generation module with multi-path graph attention mechanism is designed to learn semantic relationships among objects based on the initial graph. Finally, a saliency ranking prediction module dynamically adopts the learned scene context through a novel graph hypernetwork, for inferring the saliency rankings. Experimental results show that our HyperSOR can significantly improve the performance of SOR.