The complex information encoded into the element connectivity of a system gives rise to
the possibility of graphical processing of divisible systems by using the Graph theory. An application in this sense is the
quantitative characterization of molecule topologies of drugs, proteins and nucleic acids, in order to build mathematical
models as Quantitative Structure - Activity Relationships between the molecules and a specific biological activity. These
types of models can predict new drugs, molecular targets and molecular properties of new molecular structures with an
important impact on the Drug Discovery, Medicinal Chemistry, Molecular Diagnosis, and Treatment. The current review
is focused on the mathematical methods to encode the connectivity information in three types of graphs such as star
graphs, spiral graphs and contact networks and three in-house scientific applications dedicated to the calculation of
molecular graph topological indices such as S2SNet, CULSPIN and MInD-Prot. In addition, some examples are
presented, such as results of this methodology on drugs, proteins and nucleic acids, including the Web implementation of
the best molecular prediction models based on graphs.
Keywords: Molecular information, QSAR, Markov descriptors, graphs, complex networks, protein topological indices.
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