Network

The urban web is a complex organizing structure that exists primarily in the space between buildings. Each building encloses and shelters one or more human activity nodes… The urban web consists of all exterior and connective elements such as pedestrian and green areas, free-standing walls, footpaths, and roads of increasing capacity from a bicycle path up to an expressway. Empirical observations verify that the stronger the connections, and the more substructure the web has, the more life a city has… 1

The network of streets which is the base on which cities grow and change is clearly not a small world. Street networks are planar graphs composed of junctions and street segments with junctions usually having a small in-degree and out-degree, usually no more than 6 with a mean of around 4. 3

It is important to mention that it has been observed that the distribution of the number of connections (the degree distribution) of the vertices of the dual representation of street networks is often scale-free. 2

Recent investigations into the connectivity of urban form lead us to conclude that a functioning urban fabric — a living neighborhood — is connected by paths that obey an inverse power-law distribution. The most successful urban regions all over the world are found to have a great range of connections, from footpaths, to bicycle paths, to low-traffic roads, to through roads, up to expressways; in decreasing number. The data comes indirectly from measuring the fractal structure of urban connective networks, which implies an inverse power-law distribution according to both the length and width of individual paths (corresponding to the intensity of traffic flow). 4

The linear decay of the intersection density [of the London street network]… that is related to the city’s suburban growth, can be taken into consideration as a signature of the phenomena called urban sprawl. 2

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Quite suddenly we reach a threshold where every node is connected to every other directly or indirectly and the average distance travelled from any node to any other stabilises. This is the critical threshold. After this, adding links does not change the distance very much. 3

See Also: Assemblage, Shortest Path, Infrastructure