Facial expressions demonstrate the important information about our emotions and show the real intentions. In this study, a novel texture transformation method using graph structures is presented for facial expression recognition. Our proposed method consists of five steps. First the face image is segmented and resized. Then the proposed graph-based texture transformation is used as feature extractor. The exemplar feature extraction is performed using the proposed deep graph texture transformation. The extracted features are concatenated to obtain one dimensional feature set. This feature set is subjected to maximum pooling and principle component analysis methods to reduce the number of features. These reduced features are fed to classifiers and we have obtained the highest classification accuracy of 97.09% and 99.25% for JAFFE and TFEID datasets respectively Moreover, we have used CK + dataset to obtain comparison results and our textural transformation based model yielded 100% classification accuracy on the CK + dataset. The proposed method has the potential to be employed for security applications like counter terrorism, day care, residential security, ATM machine and voter verification.