Signal transduction pathways play important roles in various biological processes such as cell cycle, apoptosis, proliferation, differentiation and responses to the extal stimuli. Efficient computational methods are of great demands to map signaling pathways systematically based on the interactome and microarray data in the post-genome era. This paper proposes a novel approach to infer the pathways based on the network flow well studied in the operation research. The authors define a potentiality variable for each protein to denote the extent to which it contributes to the objective pathway. And the capacity on each edge is not a constant but a function of the potentiality variables of the corresponding two proteins. The total potentiality of all proteins is given an upper bound. The approach is formulated to a linear programming model and solved by the simplex method. Experiments on the yeast sporulation data suggest this novel approach recreats successfully the backbone of the MAPK signaling pathway with a low upper bound of the total potentiality. By increasing the upper bound, the approach successfully predicts all the members of the Mitogen-activated protein kinases (MAPK) pathway responding to the pheromone. This simple but effective approach can also be used to infer the genetic information processing pathways underlying the expression quantitative trait loci (eQTL) associations, illustrated by the second example.