We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to its graph representations known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general, mathematically justifiable, and they put vertex simplification and hyperedge simplification in a unifying framework.

中文翻译：

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超图的拓扑简化

我们通过拓扑简化研究超图可视化。我们使用来自拓扑数据分析的工具探索超图的顶点简化和超边简化。特别是，我们将一个超图转换为它的图形表示形式，即折线图和集团扩展。这种图表示的拓扑简化导致超图的简化。在简化超图时，如果顶点属于几乎相同的一组超边，我们就可以对其进行合并；如果共享几乎相同的一组顶点，则可以对这些超边进行合并。我们提出的方法是通用的，在数学上是合理的，并且将顶点简化和超边简化置于统一框架中。