Objectives:To propose an automatic signature identification for off-line signature utilising graph theory approaches. Methods: Scanned signatures (Kaggle, https://www.kaggle.com/divyanshrai/handwritten-signatures/data) are collected for off-line signature data. The method follows pre-processing, vertex point extraction by midpoint traverse method, features extraction using edge, average edge and average edge D-distance and Support Vector Machine (SVM) to classify and predict the true label for the genuine and forged signatures. False Acceptance Ratio (FAR) and False Rejection Ratio (FRR) give the accuracy of the proposed methods. This off-line signature verification method is compared with the deep learning techniques existing in the literature. Findings: Support Vector Machine (SVM) used for classification and results on standard signature datasets like ICDAR (International Conference on Document Analysis and Recognition). The results demonstrate how the proposed strategy outperforms the state-of-the-art already available. Novelty: The proposed approach use the edge distance, average edge distance, and average edge D-distance inbuilt graph structures to extract the feature points. Keywords: Signature images; grid approach; bipartite graph; complete bipartite graph; mid point traverse method Methodology Proposed methodThis section proposes an off-line signature automatic identification method that can be used to identify the signature's authenticity https://www.indjst.org/