Santiago, Oscar MartínezMarrero-Ponce, YovaniCabrera, Reisel MillánBarigye, Stephen J.Martínez, Luis M. Artiles2023-02-092023-02-092015Martinez Santiago, O., Marrero-Ponce, Y., Millán Cabrera, R., Barigye, S. J., Martinez-Lopez, Y., Artiles Martínez, L. M., ... & Torrens, F. (2015). Extending graph (discrete) derivative descriptors to n-tuple atom-relations. Match-Communications in Mathematical and in Computer Chemistry, 2015, vol. 73, num. 2, p. 397-420.0340 - 6253https://nru.uncst.go.ug/handle/123456789/7676In the present manuscript, an extension of the previously defined Graph Derivative Indices (GDIs) is discussed. To achieve this objective, the concept of a hypermatrix, conceived from the calculation of the frequencies of triple and quadruple atom relations in a set of connected sub-graphs, is introduced. This set of subgraphs is generated following a predefined criterion, known as the event (S), being in this particular case the connectivity among atoms. The triple and quadruple relations frequency matrices serve as a basis for the computation of triple and quadruple discrete derivative indices, respectively. The GDIs are implemented in a computational program denominated DIVATI (acronym for DIscrete DeriVAtive Type Indices), a module of TOMOCOMD-CARDD program. Shannon‟s entropy-based variability analysis demonstrates that the GDIs show major variability than others indices used in QSAR/QSPR researches. In addition, it can be appreciated when the indices are extended over n-elements from the graph, its quality increases, principally when they are used in a combined way.enDiscreteN-Tuple Atom-RelationsGraph Derivative IndicesArticle