The structure of urban networks

Cities are located at the crossroads of many different networks. These networks are physical entities such as infrastructures that enable movements of individuals, transportation of goods, and distribution of electricity, gas and water, but can also be virtual, such as the social and professional networks. In modern countries, these networks have evolved over a long time (sometimes centuries), have become very complex and display a large variety of elements and actors in their functioning. This complexity leads to the relatively unexpected result that their robustness is not very well understood, as demonstrated by the occurrence of large blackouts in 2003 in North America. In addition, many of these networks are coupled to each other, which changes their resilience behavior (Buldyrev et al. 2010), and indicates the importance of considering multilayer networks (Vivela et al. 2014) for understanding their fragility. Measuring the structure and evolution of these infrastructures is therefore fundamental for understanding and modeling the resilience of cities and for understanding the socio-economic processes that govern its functioning. We focus here on physical networks, such as transportation systems where nodes are stations and links represent segments between consecutive stations. In particular, an important component of cities is the street network made of nodes that represent the intersections, and the links are segments of roads between consecutive intersections. These networks can be thought of as a simplified schematic view of cities, but which captures a large part of their structure and organization (Southworth and Ben-Joseph 2003), and contains a large amount of information about underlying and universal mechanisms at play in their formation and evolution. Identifying the main mechanisms in these systems is not a new task (Haggett and Chorley 1969; Xie and Levinson 2011), but the recent availability of digitalized maps, historical or contemporary, allows us to test ideas and models on large-scale cross-sectional and historical data. Understanding these networks is therefore a central task for constructing a quantitative science of cities (Barthelemy 2016; Batty 2013).