Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph structures, even for moderately sized data of a few hundred nodes, due to visual clutter. We propose to 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 {\mog}, 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. We provide a software tool that enables interactive explorations of such skeletons and demonstrate the effectiveness of our method for synthetic and real-world data.

翻译：节点-链接图是表示个体、企业、蛋白质及通信端点间关系的常用图可视化方法。然而，即使对于仅含数百个节点的中等规模数据，节点-链接图也可能因视觉杂乱而无法有效传达图的结构特征。本文提出将拓扑数据分析中的经典工具——Mapper构造——应用于图可视化，该方法为在保留核心结构的同时进行数据抽象提供了坚实的理论基础。我们针对加权无向图开发了一种名为{\mog}的Mapper构造变体，可生成保持同调性的骨架。进一步证明，通过调整单一参数即可实现输入图的多尺度骨架化。我们提供了支持交互式探索此类骨架的软件工具，并通过合成数据与实际数据验证了该方法的有效性。