Background: Metabolic pathway is a highly regulated network consisting of many metabolic reactions involving substrates, enzymes, and products, where substrates can be transformed into products with particular catalytic enzymes. Since experimental determination of the network of substrate-enzyme-product triad (whether the substrate can be transformed into the product with a given enzyme) is both time-consuming and expensive, it would be very useful to develop a computational approach for predicting the network of substrate-enzyme-product triads. Results: A mathematical model for predicting the network of substrate-enzyme-product triads was developed. Meanwhile, a benchmark dataset was constructed that contains 744,192 substrate-enzyme-product triads, of which 14,592 are networking triads, and 729,600 are non-networking triads; i.e., the number of the negative triads was about 50 times the number of the positive triads. The molecular graph was introduced to calculate the similarity bet...