The management of moving objects has been intensively studied in the recent years. A wide and increasing range of database applications has to deal with spatial objects whose position changes continuously over time, called moving objects. Due to the continuous and unpredictable nature of the movements, they cannot be precisely stored in a database, and therefore objects' positions are sampled, and between these sampled positions interpolation is used. This sampling/interpolation approach results in uncertainty in the objects' positions in the whole trajectory of the moving objects. In this paper, we try to analyze this problem about uncertainty when the movement is restricted to a network. Examples of such movements are cars in highways and trains in railroads. The uncertainty problem is simpler in such cases compared to the free movement in 2-dimensional space. We describe the geometry of the uncertain trajectories of the objects with movement constrained to networks, an ex...