The process of extracting a curve-skeleton from a 3D object is critical for various computer vision applications, including 3D object matching and recognition, 3D object segmentation, 3D animation, and 3D surface reconstruction. In this paper, we present a novel and efficient method for extracting the skeleton from general 3D objects based on a weight graph representation. Our method defines a unique spiral patch for each graph vertex, representing the shortest loop over the surface contour starting from the vertex. We construct a curve skeleton graph (CSG) using these spiral patches, which accurately represents the skeleton. We demonstrate the robustness of our method through various experiments, including noise reduction and different transformations. Furthermore, we showcase two practical applications based on our method: shape partitioning and gesture recognition. Our approach outperforms existing methods, demonstrating superior accuracy and efficiency. Overall, our proposed method presents a robust and efficient solution for extracting a curve-skeleton from general 3D objects, with promising applications in various computer vision fields.