We propose a method for image categorization and retrieval that leverages graphs and a graph attention network (GAT)-based autoencoder. Our approach is representative-centric, that is, we execute the categorization and retrieval process via the representative models we construct for the images and image categories. We utilize a graph where nodes represent images (or their representatives) and edges capture similarity relationships. GAT highlights important features and relationships between images, enabling the autoencoder to construct context-aware latent representations that capture the key features of each image relative to its neighbors. We obtain category representatives from these embeddings and categorize a query image by comparing its representative to the category representatives. We then retrieve the most similar image to the query image within its identified category. We demonstrate the effectiveness of our representative-centric approach through experiments with both the GAT autoencoders and standard feature-based techniques.