Intrinsic Graph Distances Compared to Euclidean Distances for Correspondent Graph Embedding

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors computed either from the molecular graph or from the three-dimensional (3D) molecular geometry. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, similarity and diversity assessment, and quantitative structure-activity relationships. In recent years a large variety of topological indices were derived from different sorts of graph distance functions which have been considered to characterize the molecular shape and structure. These include not only the shortest-path distance but also the resistance distance and the quasi-Euclidean distance. A comparison is made between five intrinsic graph distance functions and the geometric distance for a set of benzenoid hydrocarbons. Overall, a very good correlation is obtained for all graph distances, indicating that the graph descriptors derived from them capture some part of the 3D information of the molecular structure. INTRODUCTION Professor Alexandru T. Balaban (Sandy) is one of the early developers and proponents of the field of topological indices (TIs) which are chemical descriptors derived from the # Dedicated on the occasion of the 70 birthday to Professor Alexandru T. Balaban, who has long pursued the use of topological indices as QSAR and QSPR descriptors