Fig. 2
Network construction The graphs are generated considering the metabolites as nodes, with edges connecting metabolites involved in the same reaction, one as a reagent and the other one as the product. a Representation of a metabolic model as a set of reactions. b For each reaction and each gene/enzyme catalyzing it, we consider all the (source, target) couples of involved metabolites. c The network for the metabolic model is obtained by linking each node representing a source metabolite with the node representing the corresponding target metabolite, with as many links as there are enzymes catalyzing the reaction. d Data for each patient (e.g., patient P1) is given by the relative gene expression values of the sample, e that are used for weighting the corresponding edges. f The obtained multigraphs are reduced to simple graphs, where weights are computed by averaging the gene expression values in the same reaction and adding these means in the case of different reactions. For example, the edges between the source metabolite M1 and the target metabolite M4 are reduced to a single edge whose weight (0.3) is computed by adding the average (0.2) of the weights for the two yellow links with the weight (0.1) of the orange link