Transit network design problem (TNDP) usually needs a recursive solution to successive transit assignment problems. Interestingly, the transit assignment problem is complicated with several unique criteria. In this study, we comprehensively review two well-known graphical transit assignment models from the literature. The first model is based on the hypergraph theory by Spiess and Florian (1989), and the second is the section transit network representation of De Cea and Fernandez (1993). The two assignment approaches are formulated in a single mathematical notation framework for the first time in the literature to understand the inherent differences better. We aim to bring attention again to these approaches for the upcoming TNDP studies since the most used transit assignment models in the TNDP are deficient in their basic assumptions compared with the considered models.