
Rücker's walk count (WC) indices are wellknown topological indices (TIs) used in Chemoinformatics to quantify the molecular structure of drugs represented by a graph in Quantitative structureactivity/property relationship (QSAR/QSPR) studies. In this work, we introduce for the first time the higherorder (kth order) analogues (WCk) of these indices using Markov chains. In addition, we report new QSPR models for large complex networks of different BioSystems useful in Parasitology and Neuroinformatics. The new type of QSPR models can be used for model checking to calculate numerical scores S(Lij) for links Lij (checking or reevaluation of network connectivity) in large networks of all these fields. The method may be summarized as follows: (i) first, the WCk(j) values are calculated for all jth nodes in a complex network already created; (ii) A linear discriminant analysis (LDA) is used to seek a linear equation that discriminates connected or linked (Lij=1) pairs of nodes experimentally confirmed from nonlinked ones (Lij=0); (iii) The new model is validated with external series of pairs of nodes; (iv) The equation obtained is used to reevaluate the connectivity quality of the network, connecting/disconnecting nodes based on the quality scores calculated with the new connectivity function. The linear QSPR models obtained yielded the following results in terms of overall test accuracy for reconstruction of complex networks of different BioSystems: parasitehost networks (93.14%), NW Spain fasciolosis spreading networks (71.42/70.18%) and CoCoMac Brain Cortex coactivation network (86.40%). Thus, this work can contribute to the computational reevaluation or model checking of connectivity (collation) in complex systems of any science field.
