Randic connectivity index (X1) is a well known quantitative measure of connectedness patterns in molecular graphs, as developed by Randic. This index has been demonstrated to be a successful predictor in quantitative structure – activity/property studies for molecules. Different authors have used X1 to predict carbonic anhydrase inhibitors, lipophilicity of polyacenes or variation of toxic effects over species. In 1999, Bermudez and Daza extended X1 in order to characterize the tRNA structures of Escherichia coli using the graph theory. More recently, Munteanu et al. used X1 to seek natural/random protein classification models based on star network topological indices.
On the other hand, Markov chains theory have been used by our group to generate different classes of topological indices and centrality measures for nodes in complex networks. Therefore, it is very interesting to use Markov chains in the generalization of X1 in order to create a new family of higher order analogues that may encode new and relevant information about the complex systems.
In this work, we introduced new Markov-Randic centralities that may be used to study Biology, Parasitology, Technology, Social and Law Networks. A comparison of the X1 for co-aggregation, Fasciolosis, financial law, biochemical, brain pathways, yeast, US Airlines, dolphins, E. coli, drug policy, football and Dutch elite networks, and the evolution of X1 during irreversible network attack are presented.