Background Histological feature representation is advantageous for computer aided diagnosis (CAD) and disease classification when using predictive techniques based on machine learning. Explicit feature representations in computer tissue models can assist explainability of machine learning predictions. Different approaches to feature representation within digital tissue images have been proposed. Cell-graphs have been demonstrated to provide precise and general constructs that can model both low- and high-level features. The basement membrane is high-level tissue architecture, and interactions across the basement membrane are involved in multiple disease processes. Thus, the basement membrane is an important histological feature to study from a cell-graph and machine learning perspective. Results We present a two stage machine learning pipeline for generating a cell-graph from a digital H &E stained tissue image. Using a combination of convolutional neural networks for visual analysis and graph neural networks exploiting node and edge labels for topological analysis, the pipeline is shown to predict both low- and high-level histological features in oral mucosal tissue with good accuracy. Conclusions Convolutional and graph neural networks are complementary technologies for learning, representing and predicting local and global histological features employing node and edge labels. Their combination is potentially widely applicable in histopathology image analysis and can enhance explainability in CAD tools for disease prediction.