Graph neural network (GNN) has powerful representation ability, but optimal configurations of GNN are non-trivial to obtain due to diversity of graph structure and cascaded nonlinearities. This paper aims to understand some properties of GNN from a computer vision (CV) perspective. In mathematical analysis, we propose an adaptive GNN model by recursive definition, and derive its relation with two basic operations in CV: filtering and propagation operations. The proposed GNN model is formulated as a label propagation system with guided map, graph Laplacian and node weight. It reveals that 1) the guided map and node weight determine whether a GNN leads to filtering or propagation diffusion, and 2) the kernel of graph Laplacian controls diffusion pattern. In practical verification, we design a new regularization structure with guided feature to produce GNN-based filtering and propagation diffusion to tackle the ill-posed inverse problems of quotient image analysis (QIA), which recovers the reflectance ratio as a signature for image analysis or adjustment. A flexible QIA-GNN framework is constructed to achieve various image-based editing tasks, like face illumination synthesis and low-light image enhancement. Experiments show the effectiveness of the QIA-GNN, and provide new insights of GNN for image analysis and editing.