The newly emerging field of Network Science deals with the tasks of modelling, comparing and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a twodimensional array, graph theory and applied linear algebra provide extremely useful tools. Here, we focus on the general concepts of centrality, communicability and betweenness, each of which quantifies important features in a network. Some recent work in the mathematical physics literature has shown that the exponential of a network’s adjacency matrix can be used as the basis for defining and computing specific versions of these measures. We introduce here a general class of measures based on matrix functions, and show that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments. We also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clustering and ordering. We finish with computational examples showing the new matrix resolvent version applied to real networks.

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Abstract: In a multi-target complex network, the links (Lij) represent the interactions between the drug (di) and the target (tj), characterized by different experimental measures (Ki, Km, IC50, etc.) obtained in pharmacological assays under diverse boundary conditions (cj). In this work, we handle Shannon entropy measures for developing a model encompassing a multi-target network of neuroprotective/neurotoxic compounds reported in the CHEMBL database. The model predicts correctly>8300 experimental outcomes with Accuracy, Specificity, and Sensitivity above 80%–90 % on training and external validation series. Indeed, the model can calculate different outcomes for>30 experimental measures in>400 different experimental protocolsin relation with>150 molecular and cellular