The stochastic cloud cover on photovoltaic (PV) panels affects the solar power outputs, producing high instability in the integrated power systems. It is an effective approach to track the cloud motion during short-term PV power forecasting based on data sources of satellite images. However, since temporal variations of these images are noisy and non-stationary, pixel-sensitive prediction methods are critically needed in order to seek a balance between the forecast precision and the huge computation burden due to a large image size. Hence, a graphical learning framework is proposed in this study for intra-hour PV power prediction. By simulating the cloud motion using bi-directional extrapolation, a directed graph is generated representing the pixel values from multiple frames of historical images. The nodes and edges in the graph denote the shapes and motion directions of the regions of interest (ROIs) in satellite images. A spatial-temporal graph neural network (GNN) is then proposed to deal with the graph. Comparing with conventional deep-learning-based models, GNN is more flexible for varying sizes of input, in order to be able to handle dynamic ROIs. Referring to the comparative studies, the proposed method greatly reduces the redundancy of image inputs without sacrificing the visual scope, and slightly improves the prediction accuracy.