Moving human-computer interaction off the desktop and into our cities requires new approaches to understanding people and technologies in the built environment. We approach the city as a system, with human, physical and digital components and behaviours. In creating effective and usable urban pervasive computing systems, we need to take into account the patterns of movement and encounter amongst people, locations, and mobile and fixed devices in the city. Advances in mobile and wireless communications have enabled us to detect and record the presence and movement of devices through cities. This article makes a number of methodological and empirical contributions. We present a toolkit of algorithms and visualization techniques that we have developed to model and make sense of spatial and temporal patterns of mobility, presence, and encounter. Applying this toolkit, we provide an analysis of urban Bluetooth data based on a longitudinal dataset containing millions of records associated with more than 70000 unique devices in the city of Bath, UK. Through a novel application of established complex network analysis techniques, we demonstrate a significant finding on the relationship between temporal factors and network structure. Finally, we suggest how our understanding and exploitation of these data may begin to inform the design and use of urban pervasive systems.