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

Pablo      Riera-Fernandez; Cristian   R.   Munteanu; Raquel      Martin-Romalde; Aliuska      Duardo-Sanchez; Humberto      Gonzalez-Diaz

Abstract

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-Randi indices of order k-th (¹χk). Later, we applied these new indices to seek models useful to calculate numerical quality scores S(L_ij) for network links L_ij (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.

Keywords: Brain cortex networks, complex networks, connectome, disease spreading networks, legal-social networks, markov chains, metabolic reactions networks, quantitative structure-property relationships, topological indices.