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06092032 Wang, Hua On the Wiener index: an edge version v.s. the original. Bull. Inst. Comb. Appl. 63, 101-108 (2011). 2011 The Institute of Combinatorics and its Applications, Winnipeg EN topological indices edge-Wiener index molecular structure Zbl 1224.05144 Summary: As one of the topological indices used to correlate chemical compounds' molecular structures with physical properties, the Wiener index $W$ (sum of the distances between vertices) has been extensively studied by both mathematicians and chemists. Recently {\it A. Iranmanesh}, {\it I. Gutman}, {\it O. Khormali} and {\it A. Mahmiani} [MATCH Commun. Math. Comput. Chem. 61, No. 3, 663--672 (2009; Zbl 1224.05144)] proposed and examined several potential edge versions of the Wiener index. In this note we take a recommended edge-Wiener index $(W_e)$ and explore it's relationship with $W$. In particular, we provide explicit correlations for some graphs that have frequent appearances in the study of the Wiener index.