This thesis discusses how neural networks for graphs can be used to predict dynamical properties of biochemical pathways and to gain insights concerning the role of their structure. For this purpose, two datasets about the properties of monotonic influence and sensitivity have been designed, created and tested on a well-known model. The obtained results have been further extended by performing ablation tests on the newly introduced properties as well as on a previous work concerning robustness. Moreover, an approach to understand the possible role of arcs in biochemical pathways has been introduced providing examples of its application. Performed analyses have not only confirmed the successful application of neural networks for graphs within this domain, but have also provided interesting novel results about the structure of biochemical pathways.