Traffic flow data are a significant component of most intelligent transportation systems (ITS). Complete traffic flow data are required for most ITS applications, but providing traffic sensors in all network streets is not practical. Some flow types are difficult to observe directly, such as node pair demand (O/D flow). This study provides a mathematical analysis approach using a factorization scheme to convert conventional traffic assignment mapping into a useful format. The new mapping structure helps in identifying the amount of traffic-counting data (link flows) necessary to solve either the full observability problem for the network or a partial one. Once the required data are provided, the observability problem can be easily solved using backward substitution. In addition, the new format provides the dependencies of the different flow measures in the network. The proposed approach can track the change in the network observability state with the route choice uncertainty. Two fully reported illustrative examples in addition to a real case network are presented to demonstrate the generality of the proposed method and its potential contribution to the observability problem.