Saliency object ranking (SOR) has attracted significant attention recently. Previous methods usually failed to explicitly explore the saliency degree-related relationships between objects. In this paper, we propose a novel Domain Separation Graph Neural Network (DSGNN), which starts with separately extracting the shape and texture cues from each object, and builds an shape graph as well as a texture graph for all objects in the given image. Then, we propose a Shape-Texture Graph Domain Separation (STGDS) module to separate the task-relevant and irrelevant information of target objects by explicitly modelling the relationship between each pair of objects in terms of their shapes and textures, respectively. Furthermore, a Cross Image Graph Domain Separation (CIGDS) module is introduced to explore the saliency degree subspace that is robust to different scenes, aiming to create a unified representation for targets with the same saliency levels in different images. Importantly, our DSGNN automatically learns a multi-dimensional feature to represent each graph edge, allowing complex, diverse and ranking-related relationships to be modelled. Experimental results show that our DSGNN achieved the new state-of-the-art performance on both ASSR and IRSR datasets, with large improvements of 5.2\% and 4.1\% SA-SOR, respectively. Our code is provided in https://github.com/Wu-ZJ/DSGNN