Markov-Randic Indices for QSPR Re-Evaluation of Metabolic, Parasite- Host, Fasciolosis Spreading, Brain Cortex and Legal-Social Complex Networks

The Randic index is a well known topological index (TI) used in QSAR/QSPR studies to quantify the molecular structure represented by a graph. In this work we review some aspects of this TI with special emphasis on the generalizations introduced by Kier & Hall and more recently by Estrada. Next, we introduced a new generalization using a Markov chain in order to obtain a new family of TIs called the Markov-Randic indices of order k-th (1χk). Later, we applied these new indices to seek models useful to calculate numerical quality scores S(Lij) for network links Lij (connectivity) in known complex networks. The linear models obtained produced the following results in terms of overall accuracy for network re-construction: Metabolic networks (70.48%), Parasite-Host networks (90.86%), CoCoMac brain cortex co-activation network (81.59%), NW Spain Fasciolosis spreading network (99.04%). Spanish financial law network (71.83%). This work opens a new door to the computational re-evaluation of network connectivity quality (collation) in different complex systems.