Moving objects can be tracked with sensors such as RFID tags or GPS devices. Their movement can be represented as sequences of time-stamped locations. Studying such spatio-temporal movement sequences to discover spatial sequential patterns holds promises in many real-world settings. A few interesting applications are customer shopping traverse pattern discovery, vehicle traveling pattern discovery, and route prediction. Traditional spatial data mining algorithms suitable for the Euclidean space are not directly applicable in these settings. We propose a new algorithm to cluster movement paths such as shopping trips for pattern discovery. In our work, we represent the spatio-temporal series as sequences of discrete locations following a pre-defined network. We incorporate a modified version of the Longest Common Subsequence (LCS) algorithm with the network structure to measure the similarity of movement paths. With such spatial networks we implicitly address the existence of spatial obstructs as well. Experiments were performed on both hand-collected real-life trips and simulated trips in grocery shopping. The initial evaluation results show that our proposed approach, called Net-LCSS, can be used to support effective and efficient clustering for shopping trip pattern discovery.