Skeletonization, also called thinning, is an importantpre-processing step in computer vision and image processing tasks such as shape analysis and vectorization.It is a morphological process that generates a skeleton from an input image. Many thinning algorithms have been proposed, but accurate and fast algorithms are still in demand. In this paper, we propose a novel algorithm using embedded topological graphs and computational geometry that can extract skeletons from input binary images. We compare three well-known thinning algorithms with our method, with the experimental results showing effectiveness of the proposed method and algorithms.