Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper On Graphs
We apply the mapper construction—a popular tool in topological data analysis—to graph visualization, which provides a strong theoretical basis for summarizing the data while preserving their core structures. We develop a variation of the mapper construction targeting weighted, undirected graphs, called Mapper on Graphs, which generates homology-preserving skeletons of graphs. We further show how the adjustment of a single parameter enables multi-scale skeletonization of the input graph. Finally, we provide a software tool that enables interactive explorations of such skeletons and demonstrates the effectiveness of our method for synthetic and real-world data.
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