To understand the rheological behavior of fibrin clots, we must obtain quantitative measurements of morphometric parameters of the networks formed under various conditions. The networks are so complex that researchers must currently manually segment the images of network samples and estimate the parameters from them. Skeletonization is a promising tool for automating this task. We here propose a method that rapidly constructs a coarse representation of a skeleton graph and, using the snake model, deforms the graph to obtain smooth skeletons. Unlike many existing approaches, our method does not involve explicit object boundary information or high order derivatives. Since our method processes a given image as a whole, the presence of multiple objects in an image is automatically detected and the skeletons of these objects are computed simultaneously.