Mathematical analysis of urban spatial networks

2009-01 till 2012-10
Research Areas: 

The speed and scale of urban growth require urgent global actions to help cities prepare for growth and to avoid that they will become the future epicenters of poverty and human suffering. Physical segregation of minority groups dispersed over the spatially isolated pockets of streets, and other inner-city areas that are socially barricaded by railways and industries cause their economic marginalization. In existing cities, efforts should be made to reconnect isolated districts, perhaps by building tunnels and bridges.

Methods and Research Questions: 

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill, providing a neat way to spot the signs of urban decay before it happens. Cities can be considered to be among the largest and most complex artificial networks created by human beings. At the same time the city is the ever-biggest communication editor that determines not only our present social and economic well being but that for those generations to come provides an interface for our everyday mutual interactions. Sociologists think that isolation worsens an area's economic prospects by reducing opportunities for commerce, and engenders a sense of isolation in inhabitants, both of which can fuel poverty and crime. Unfortunately, urban planners and governments have often failed to take such isolation into account when shaping the city landscape, not least because isolation can sometimes be difficult to quantify in the complex fabric of a major city. Many neighborhoods are cut off from other parts of the city by poor transport links and haphazard urban planning, which can often lead to social ills. By spatial organization of urban space, we can create new rules for how neighborhoods where people can move and meet other people face-to face by chance fit together on a large scale in public places (such as office buildings, shops, hospitals, etc.). Due to the numerous and diverse human-driven activities, urban network topology and dynamics can differ quite substantially from that of natural networks and so call for an alternative method of analysis. Spatial networks of human settlements are not random; they take the form of a complicated highly inhomogeneous structure that emerges due to trade-offs - the optimization problems between the multiple, complicated and probably conflicting objectives. In our work, we have laid down the theoretical foundations for studying the topology of compact urban patterns, using methods from spectral graph theory and statistical physics. These methods are demonstrated as tools to investigate the structure of a number of real cities with widely differing properties: medieval German cities, the webs of city canals in Amsterdam and Venice, and a modern urban structure such as found in Manhattan. In particular, we have found that random walks on spatial city graphs spot hidden areas of geographical isolation in the urban landscape, such as the Ghetto of Venice and the Bowery and Harlem (New York) which are isolated from nearby areas. Random walks convert a graph into metric Euclidean space; we use this natural metric in order to explore the network community structure and to construct its visual representations.


Urbanization has been the dominant demographic trend in the entire world, during the last century. The essentially fast growth of cities in the last decades urgently calls for a profound insight into the common principles stirring the structure of urban development all over the world. The outcome of the MAUS project is an interdisciplinary approach to the understanding of how people use urban space and how a global strongly inhomogeneous urban network determines the quality of human life by providing space that people can use. The specific outcomes of the project are (1) the corpuses of empirical data on the structure of urban networks in cities of Germany, Holland, France, and the USA; (2) the robust recommendation engines for urban planning and environment, the vital issue of human sustainability; (3) the robust recommendation engines for the expedient land use and feasible logistic. The need could not be more urgent and the time could not be more opportune, to act now to sustain our common future.