Taxicabs equipped with real-time location sensing devices are increasingly becoming popular. Such location traces are a rich source of information and can be used for congestion pricing, taxicab placement, and improved city planning. An important problem to enable these application is to identify human mobility patterns from the taxicab traces, which translates to being able to identify pickup and drop off points for a particular trip. In this paper, we show that while past approaches are effective in detecting hotspots using location traces, they are largely ineffective in identifying trips (pairs of pickup and drop off points). We propose the use of a graph theory concept - stretch factor in a novel manner to identify trip(s) made by a taxicab and show that a Hidden Markov Model based algorithm can identify trips (using real datasets from taxicab deployments in Shanghai and partially simulated datasets from Stockholm) with precision and recall of 90-94% -, a significant improvement over past approaches that result in a precision and recall of about 50-60%.