Criteria for ranking (poly)cyclic chemical constitutional graphs and their vertices via centrality measures

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.