Identifying changes in the spatial structure of cities is a prerequisite for the development and validation of adequate planning strategies. Nevertheless, current methods of measurement are becoming ever more challenged by the highly diverse and intertwined ways of how people actually make use of urban space. Here, we propose a new quantitative measure for the centrality of locations, taking into account not only the numbers of people attracted to different locations, but also the diversity of the activities they are engaged in. This ‘centrality index’ allows for the identification of functional urban centres and for a systematic tracking of their relative importance over time, thus contributing to our understanding of polycentricity. We demonstrate the proposed index using travel survey data in Singapore for different years between 1997 and 2012. It is shown that, on the one hand, the city-state has been developing rapidly towards a polycentric urban form that compares rather closely with the official urban development plan. On the other hand, however, the downtown core has strongly gained in its importance, and this can be partly attributed to the recent extension of the public transit system.