The medical imaging and image processing techniques, ranging from microscopic to macroscopic, has become one of the main components of diagnostic procedures to assist dermatologists in their medical decision-making processes. Computer-aided segmentation and border detection on dermoscopic images is one of the core components of diagnostic procedures and therapeutic interventions for skin cancer. Automated assessment tools for dermoscopic images have become an important research field mainly because of inter- and intra-observer variations in human interpretations. In this study, a novel approach-graph spanner-for automatic border detection in dermoscopic images is proposed. In this approach, a proximity graph representation of dermoscopic images in order to detect regions and borders in skin lesion is presented.