Graph parameters and topological indices allow a discussion about hierarchical criteria for ranking monocyclic and polycyclic molecular (constitutional) chemical graphs. For brevity, chemical constitutional graphs will be referred to as CGs. These criteria include the number of vertices (graph order), cyclomatic numbers, vertex degrees (from one to four), number of polygons with increasing numbers of edges (3-, 4-, 5-gons, etc.), and vicinity with vertices of increasing rank. A similar hierarchy can be established for ranking vertices in a CG, and a detailed discussion is presented for ordering vertices in all seven identity CGs with 6 vertices and in 25 from the many identity CGs with 7 vertices. This is the first discussion of ranking the vertices of CGs from the viewpoint of centrality measures.

中文翻译：

---

通过中心性度量对（多）循环化学结构图及其顶点进行排序的标准

图参数和拓扑索引允许讨论对单环和多环分子（结构）化学图进行排序的层次标准。为简洁起见，化学结构图将被称为 CG。这些标准包括顶点数（图顺序）、圈数、顶点度数（从 1 到 4）、边数增加的多边形数（3、4、5 边形等），以及秩递增的顶点。可以建立类似的层次结构来对 CG 中的顶点进行排序，并详细讨论了对具有 6 个顶点的所有 7 个标识 CG 中的顶点和来自具有 7 个顶点的许多标识 CG 中的 25 个中的顶点进行排序的详细讨论。这是第一次从中心性度量的角度讨论对 CG 的顶点进行排序。