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In an era of big data and emergence of disrupting mobility technologies, statistical models have been utilized to uncover the influence of significant factors, and machine learning algorithms have been used to explore complex patterns in large datasets. Focusing on discrete choice modeling applications, this research aims to introduce computational graph (CG)-based frameworks for integrating the strengths of econometric models and machine learning algorithms. Specifically, multinomial logit (MNL), nested logit (NL), and integrated choice and latent variable (ICLV) models are selected to demonstrate the performance of the graph-oriented functional representation. Furthermore, the calculation of gradients in the log-likelihood function is accomplished using automatic differentiation (AD). Using the 2017 National Household Travel Survey data and synthetic datasets, we compare estimation results from the proposed methods with those obtained from Biogeme and Apollo. The results indicate that the CG-based choice modeling approach can produce consistent estimates of parameters with substantial computational efficiency.