oa Editorial [Hot topic: Network Topological Indices, Drug Metabolism, and Distribution (Guest Editor: H. Gonzalez-Diaz)]

Many authors have been used Graph and Complex Network theory to approach very large metabolic networks with low computational cost. These large networks are graphical representations of real metabolic systems with essentially two components nodes and links. Nodes (represented by dots) are usually metabolites, enzymes, substrates, intermediary substances, metabolic reactions or transition states. Node-to-node links (edges or arcs) express metabolic relationships between two nodes as for instance: substrate-enzyme pairs or metabolite-reaction pair. We can use these networks to describe and study all the set of metabolic processes (Metabolome) related to one organism, tissue, or diseases. Including nodes representing body compartments we can represent and study also the Absorption, Distribution, Metabolism, Excretion and Toxicity (ADMET) processes of drugs or hazardous compounds. On the other hand, other authors with a more chemical background have used graphs to represent the structure of drugs, xenobiotic substances, hazardous compounds, and metabolites. These graphs are essentially, in mathematical terms, the same objects than the metabolic networks referred in the previous paragraph. The main difference is that in molecular graphs nodes represent atoms and edges represent chemical bonds. Consequently, molecular graphs express the structure of organic compounds in terms of atom connectivity and metabolic networks represent the structure of the metabolic system in terms of metabolome connectedness. In addition, we can associate both types of graphs with different classes of numeric matrices to carry out computational studies of at the two levels of matter structural organization. The Boolean or Adjacency matrices are perhaps the more simple to explain. These matrices are square tables (number of rows = number of columns) of nxn elements, where n is the number of nodes of the system. The element matrix cell bij = 1 if the element ith link to jth in the graph. I meant, the atom ith is chemically bonded to atom jth in the structure of the drug or, for instance, the substrate ith is metabolized by the the enzyme jth. Yet we can mention a third type of complex network that lie in-between molecular graphs of drugs or metabolites and large graph of complex metabolic networks. We refer to the complex networks used to represent the 3D structures of proteins (enzymes, molecular targets, channels, receptors) involved in natural or disease metabolism or in drug ADMET processes as well. The construction of this type of graphs and matrices is straightforward to realize in an intuitive form taking into consideration the analogy between the previous situations. In these networks, aminoacids often play the role of nodes and links express spatial contact between two aminoacids (see also, contact maps or residue networks). In the same group with proteins we can find the graphs used to represent another type or biomolecules that may play also the role of enzymes, drug targets, and also participate in biological processes regulation. We refer to the graph used to represent the secondary structure (or less common the 3D structure) or RNAs. In this last class of networks, nucleotides often play the role of nodes and links express that this pair of bases are sequence neighbors or are involved in a hydrogen bond. In all these cases, we can easily calculate different invariant parameters of the matrices associated to the graphs that may be used to describe the structure of these objects (drugs, proteins, or metabolome). As this numbers are based only on connectivity information they are often named as Connectivity measures or Topological Indices (TIs). In fact, in our days, there is an explosion on the use of Topological Indices (TIs) of Graphs and Complex Networks on a broad spectrum of topics related to Drug metabolism and distribution research. One reason for the success of TIs, is the high flexibility of this theory to solve in a fast but rigorous way many apparently unrelated problems in all these disciplines. This determined the recent development of several interesting software and theoretical methods to handle with structurefunction information and data mining in this field. However, another important advantage is that: The theoretical basis is straightforward to realize for experimental scientists non-expert on computational techniques....