Urban rail transit (URT) system plays a dominating role in many megacities like Beijing and Hong Kong. Due to its important role and complex nature, it is always in great need for public agencies to better understand the performance of the URT system. This paper focuses on an essential and hard problem to estimate the network-wide link travel time and station waiting time using the automatic fare collection (AFC) data in the URT system, which is beneficial to better understand the system-wide real-time operation state. The emerging data-driven techniques, such as computational graph (CG) models in the machine learning field, provide a new solution for solving this problem. In this study, we first formulate a data-driven estimation optimization framework to estimate the link travel time and station waiting time. Then, we cast the estimation optimization model into a CG framework to solve the optimization problem and obtain the estimation results. The methodology is verified on a synthetic URT network and applied to a real-world URT network using the synthetic and real-world AFC data, respectively. Results show the robustness and effectiveness of the CG-based framework. To the best of our knowledge, this is the first time that the CG is applied to the URT. This study can provide critical insights to better understand the operational state in URT.