Texture recognition has predominantly relied on methods based on handcrafted features and more recently, on Convolutional Neural Network (CNN)-based methods. However, many of these approaches do not capture the underlying directional relationships between visual vocabularies, attributes and features. In this study, we introduce a graph-based deep learning framework for texture and material recognition called Graph Texture Network (GTN) that models the underlying directional associations among latent texture attributes, that are hierarchically related to visual texture attributes, facilitating information exchange among them and consequently improving the discriminative capability among different texture and material categories. GTN, which is a non-Euclidean data structure, provides flexibility to learn complex underlying relationships among latent texture attributes via a learnable masked adjacency matrix. To ensure robustness of GTN to noise, especially on graphs with fewer vertices, we facilitate re-calibration of self-loop edge weights to preserve salient texture information within each vertex. We then utilize residual message passing to enrich the representations of latent texture attributes. Furthermore, GTN is able to facilitate interaction across multiple graphs, representing texture information across a range of scales. Finally, GTN can be easily incorporated into a variety of CNN architectures for end-to-end training and does not require fine-tuning of pre-trained CNN backbones. Experimental results demonstrate that GTN achieves state-of-the-art performance on several benchmark texture and material datasets.