Characterizing a public transportation network, such as an urban network with multiple lines, requires the origin–destination trip counts during a given period. Yet, if automatic counting makes the embarkment (boarding) and disembarkment (alighting) counts in vehicles known, it often happens that pedestrian transfers between lines are harder to track, and require costly and invasive devices (e.g., facial recognition system) to be estimated. In this contribution, we propose a method, based on maximum entropy and involving an iterative fitting procedure, which estimates the passenger flow between origins and destinations solely based on embarkment and disembarkment counts. Moreover, this method is flexible enough to provide an adaptable framework in case additional data is known, such as attraction poles between certain nodes in the network, or percentages of transferring passengers between some lines. This method is tested on toy examples, as well as with the data of the public transportation network of the city of Lausanne provided by its Transportation Agency (tl), and gives arguably convincing estimations of the transportation flow.