Urban spatial structure in large cities is becoming ever more complex as populations grow in size, engage in more travel, and have increasing amounts of disposable income that enable them to live more diverse lifestyles. These trends have prominent and visible effects on urban activity, and cities are becoming more polycentric in their structure as new clusters and hotspots emerge and coalesce in a wider sea of urban development. Here, we apply recent methods in network science and their generalization to spatial analysis to identify the spatial structure of city hubs, centers, and borders, which are essential elements in understanding urban interactions. We use a ‘big’ data set for Singapore from the automatic smart card fare collection system, which is available for sample periods in 2010, 2011, and 2012 to show how the changing roles and influences of local areas in the overall spatial structure of urban movement can be efficiently monitored from daily transportation. In essence, we first construct a weighted directed graph from these travel records. Each node in the graph denotes an urban area, edges denote the possibility of travel between any two areas, and the weight of edges denotes the volume of travel, which is the number of trips made. We then make use of (a) the graph properties to obtain an overall view of travel demand, (b) graph centralities for detecting urban centers and hubs, and (c) graph community structures for uncovering socioeconomic clusters defined as neighborhoods and their borders. Finally, results of this network analysis are projected back onto geographical space to reveal the spatial structure of urban movements. The revealed community structure shows a clear subdivision into different areas that separate the population’s activity space into smaller neighborhoods. The generated borders are different from existing administrative ones. By comparing the results from 3 years of data, we find that Singapore, even from such a short time series, is developing rapidly towards a polycentric urban form, where new subcenters and communities are emerging largely in line with the city’s master plan. To summarize, our approach yields important insights into urban phenomena generated by human movements. It represents a quantitative approach to urban analysis, which explicitly identifies ongoing urban transformations.

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.

To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated spatio-temporal scales but when we zoom into finer scales, considerable heterogeneity and diversity is observed instead. The fundamental question we address in this paper is at what scales are the regularities we detect stable, explicable, and sustainable. This paper thus proposes a basic measure of variability to assess the stability of such regularities focusing mainly on changes over a range of temporal scales. We demonstrate this by comparing regularities in the urban mobility patterns in three world cities, namely London, Singapore and Beijing using one-week of smart-card data. The results show that variations in regularity scale as non-linear functions of the temporal resolution, which we measure over a scale from 1 minute to 24 hours thus reflecting the diurnal cycle of human mobility. A particularly dramatic increase in variability occurs up to the temporal scale of about 15 minutes in all three cities and this implies that limits exist when we look forward or backward with respect to making short-term predictions. The degree of regularity varies in fact from city to city with Beijing and Singapore showing higher regularity in comparison to London across all temporal scales. A detailed discussion is provided, which relates the analysis to various characteristics of the three cities. In summary, this work contributes to a deeper understanding of regularities in patterns of transit use from variations in volumes of travellers entering subway stations, it establishes a generic analytical framework for comparative studies using urban mobility data, and it provides key points for the management of variability by policy-makers intent on for making the travel experience more amenable.