Local descriptors have become more and more popular and are gaining a high recognition in recent years in texture analysis and other domains of image processing and computer vision due to their capability in identifying unique and distinct features which are robust to various conditions. Most of the local descriptors like local binary pattern (LBP), textons and Peano scan motif considered the neighborhood as a simple window and extracted the features. This paper derives a graph structure on a local grid. The local features are derived based on transitions between adjacent vertices. This paper derives a dual graph function using the neighborhood property that exists between a vertex V and two of its neighbors V1 and V2 which are connected with vertex V. This paper initially divides the texture image into 2 × 2 non-overlapped grids and derives dual transition function and derives a dual graph unit (DGU) and replaces the 2 × 2 grid with DGU. The co-occurrence matrix derived on DGU indexed image represents dual graph texture matrix (DGTM). The gray level co-occurrence matrix (GLCM) features are derived on DGTM, and these feature vectors are given as inputs to the machine learning classifiers for classification. The proposed local DGTM is compared with state-of-the art local-based approaches, and the results on five popular databases exhibit the efficacy of the proposed DGTM over the existing local-based methods.