Fig. 3

Visual examples of introduced adjustment methods based on transition probability. A An exemplary graph, where nodes represent metabolites (a - h) and edges are RAS values of the respective reactions (r). Although formally the reactions from nodes a to c and b to d are separate reactions with distinct reaction IDs, the RAS values of these reactions are identical because of the involvement of the exact same genes. Therefore, we denote these reactions with identical r-numbers (\(r_{1}\)) in this figure. The same also applies to edges \(r_{2}\) and \(r_{3}\). Ingoing and outgoing edges are dashed. B Edge weights are adjusted by multiplying the TP t with the RAS value of the respective reaction r. Exemplary calculations of the TPs are given for \(t_{1}\), \(t_{5}\), \(t_{6}\), and \(t_{7}\). The TP of \(t_{2}\), \(t_{3}\), \(t_{8}\), and \(t_{9}\) are equal to 1 because nodes c, d, e, and f have only one outgoing edge. C First alternative adjustment method, in which the TP is equal to 1, recursively takes the TP of the previously incoming edges. D Second alternative adjustment method, where exemplary the RAS value \(r_{3}\) is adjusted by the product of TPs along the path starting from the defined node a to node h