The explosion in the availability of GPS-enabled devices has resulted in an abundance of trajectory data. In reality, however, majority of these trajectories are collected at a low sampling rate and only provide partial observations on their actually traversed routes. Consequently, they are mired with uncertainty. In this paper, we develop a technique called InferTra to infer uncertain trajectories from network-constrained partial observations. Rather than predicting the most likely route, the inferred uncertain trajectory takes the form of an edge-weighted graph and summarizes all probable routes in a holistic manner. For trajectory inference, InferTra employs Gibbs sampling by learning a Network Mobility Model (NMM) from a database of historical trajectories. Extensive experiments on real trajectory databases show that the graph-based approach of InferTra is up to 50% more accurate, 20 times faster, and immensely more versatile than state-of-the-art techniques.