Component graphs $\Gamma_{0}(F)$ are defined for arrays of sets $F$, and in particular for arrays of path components for Vietoris-Rips complexes and Lesnick complexes. The path components of $\Gamma_{0}(F)$ are the {\it stable components} of the array $F$. The stable components for the system of Lesnick complexes $\{ L_{s,k}(X) \}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.

中文翻译：

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稳定的组件和层

分量图 $\Gamma_{0}(F)$ 是为集合 $F$ 的数组定义的，特别是为 Vietoris-Rips 复合物和 Lesnick 复合物的路径分量数组。$\Gamma_{0}(F)$ 的路径分量是数组 $F$ 的 {\it 稳定分量}。Lesnick 复合系统的稳定组件 $\{ L_{s,k}(X) \}$ 用于有限数据集 $X$ 分解为层，这些层本身就是图的路径组件。组合评分函数是为层和稳定组件定义的。