We present a new Compact Trip Representation (CTR) that allows us to manage users' trips (moving objects) over networks. These could be public transportation networks (buses, subway, trains, and so on) where nodes are stations or stops, or road networks where nodes are intersections. CTR represents the sequences of nodes and time instants in users' trips. The spatial component is handled with a data structure based on the well-known Compressed Suffix Array (CSA), which provides both a compact representation and interesting indexing capabilities. We also represent the temporal component of the trips, that is, the time instants when users visit nodes in their trips. We create a sequence with these time instants, which are then self-indexed with a balanced Wavelet Matrix (WM). This gives us the ability to solve range-interval queries efficiently. We show how CTR can solve relevant spatial and spatio-temporal queries over large sets of trajectories. Finally, we also provide experimental results to show the space requirements and query efficiency of CTR.