Before revision:  This paper compares three algorithms that solve the data skeletonisation problem for a general cloud with topological and geometric guarantees. First, the Mapper algorithm outputs a network of interlinked clusters. Second, the \alpha-Reeb algorithm discretises the classical Reeb graphand can be applied to discrete clouds at different scales \alpha. The third algorithm HoPeS produces a Homologically Persistent Skeleton without any extra parameters.
After revision:  This paper compares three algorithms that solve the data skeletonisation problem for any point cloud and guarantee a successful reconstruction. For example, given a highly noisy point sample of an unknown underlying graph, a reconstructed skeleton should be geometrically close and homotopy equivalent to (has the same number of independent cycles as) the underlying graph. One of these algorithm produces a Homologically Persistent Skeleton without any extra parameters.