D.Volchenkov
An inexorable worldwide trend toward urbanization presents an urgent need in developing a quantitative theory of urban organization and sustainable development. Town planning is not just a practice of manipulating the space, but rather an art with a far-reaching influence on society. Many aspects of urban networks substantially differ from other complex networks and call for an alternative type of analysis.
In most investigations, the relations between different components of an urban structure are frequently measured along the streets and routes considered as edges of a planar graph, while the traffic ultimate destination points and street junctions are treated as nodes. The primary graph representation of an urban network is based on relations between junctions through their streets. Being embedded into the geographical and economical landscapes, the resulting planar graphs reveal their multiple fingerprints. Among the main factors featuring the structure of graphs there are high costs of maintenance of long range connections and a scarce availability of physical space. In contrast, the dual graph representation of an urban network traces the relations between the streets through their junctions; the streets are treated as nodes, while junctions between them are represented by edges. They have been extensively studied within the concept of space syntax, an architectural theory developed in the late 1970s that seeks to reveal the mutual effects of complex spatial systems on society and vice versa. Its basic suggestion is that a spatial configuration (the system of spaces) is a driving force for human activity and cognition within urban environments. Our paper is devoted to the analysis of morphology and complexity of urban networks in their graph representations. We study several compact urban patterns: two medieval German cities (Bielefeld in Westfalia and Rothenburg ob der Tauber in Bavaria), the patterns of city canals in Venice and in Amsterdam playing the role of transport networks, and the modern urban development of Manhattan, a borough of New York City, planned in grid. A part of the results reported in the presented paper was published earlier in– we reproduce them here for clarity, while the issues of general connectivity and portraits of the cities as complex networks have never been discussed before. The fact that a connected undirected graph can be embedded into (N − 1) dimensional Euclidean space worked out in section 5 is also a novelty.
In most investigations, the relations between different components of an urban structure are frequently measured along the streets and routes considered as edges of a planar graph, while the traffic ultimate destination points and street junctions are treated as nodes. The primary graph representation of an urban network is based on relations between junctions through their streets. Being embedded into the geographical and economical landscapes, the resulting planar graphs reveal their multiple fingerprints. Among the main factors featuring the structure of graphs there are high costs of maintenance of long range connections and a scarce availability of physical space. In contrast, the dual graph representation of an urban network traces the relations between the streets through their junctions; the streets are treated as nodes, while junctions between them are represented by edges. They have been extensively studied within the concept of space syntax, an architectural theory developed in the late 1970s that seeks to reveal the mutual effects of complex spatial systems on society and vice versa. Its basic suggestion is that a spatial configuration (the system of spaces) is a driving force for human activity and cognition within urban environments. Our paper is devoted to the analysis of morphology and complexity of urban networks in their graph representations. We study several compact urban patterns: two medieval German cities (Bielefeld in Westfalia and Rothenburg ob der Tauber in Bavaria), the patterns of city canals in Venice and in Amsterdam playing the role of transport networks, and the modern urban development of Manhattan, a borough of New York City, planned in grid. A part of the results reported in the presented paper was published earlier in– we reproduce them here for clarity, while the issues of general connectivity and portraits of the cities as complex networks have never been discussed before. The fact that a connected undirected graph can be embedded into (N − 1) dimensional Euclidean space worked out in section 5 is also a novelty.
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| The city center of Bielefeld, Germany, the oldest and most compact part of the city |
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