In this paper, we propose a graph-represented image distribution similarity (GRIDS) index for full-reference (FR) image quality assessment (IQA), which can measure the perceptual distance between distorted and reference images by assessing the disparities between their distribution patterns under a graph-based representation. First, we transform the input image into a graph-based representation, which is proven to be a versatile and effective choice for capturing visual perception features. This is achieved through the automatic generation of a vision graph from the given image content, leading to holistic perceptual associations for irregular image regions. Second, to reflect the perceived image distribution, we decompose the undirected graph into cliques and then calculate the product of the potential functions for the cliques to obtain the joint probability distribution of the undirected graph. Finally, we compare the distances between the graph feature distributions of the distorted and reference images at different stages; thus, we combine the distortion distribution measurements derived from different graph model depths to determine the perceived quality of the distorted images. The empirical results obtained from an extensive array of experiments underscore the competitive nature of our proposed method, which achieves performance on par with that of the state-of-the-art methods, demonstrating its exceptional predictive accuracy and ability to maintain consistent and monotonic behaviour in image quality prediction tasks. The source code is publicly available at the following website https://github.com/Land5cape/GRIDS.