[Abstract] We can use Artificial Neural Networks (ANNs) and graph Topological Indices (TIs) to seek structure-property relationship. Balabans’ J index is one of the classic TIs for chemo-informatics studies. We used here Markov chains to generalize the J index and apply it to bioinformatics, systems biology, and social sciences. We seek new ANN models to show the discrimination power of the new indices at node level in three proof-of-concept experiments. First, we calculated more than 1,000,000 values of the new Balaban-Markov centralities Jk(i) and other indices for all nodes in >100 complex networks. In the three experiments, we found new MIANN models with >80% of Specificity (Sp) and Sensitivity (Sn) in train and validation series for Metabolic Reactions of Networks (MRNs) for 42 organisms (bacteria, yeast, nematode and plants), 73 Biological Interaction Webs or Networks (BINs), and 43 sub-networks of U.S. Supreme court citations in different decades from 1791 to 2005. This work may open a new route for the application of TIs to unravel hidden structure-property relationships in complex bio-molecular, ecological, and social networks.