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Social media generated by location-services-enabled cellular devices produce enormous amounts of location-based content. Spatiotemporal analysis of such data facilitate new ways of modeling human behavior and mobility patterns. In this paper, we use over 10 millions geo-tagged tweets from the city of Los Angeles as observations of human movement and apply them to understand the relationships of geographical regions, neighborhoods and gang territories. Using a graph based-representation of street gang territories as vertices and interactions between them as edges, we train a machine learning classifier to tell apart rival and non-rival links. We correctly identify 89% of the true rivalry network, which beats a standard baseline by about 30%. Looking at larger neighborhoods, we were able to show that distance traveled from home follows a power-law distribution, and the direction of displacement, i.e., the distribution of movement direction, can be used as a profile to identify physical (or geographic) barriers when it is not uniform. Finally, considering the temporal dimension of tweets, we detect events taking place around the city by identifying irregularities in tweeting patterns.