Networks and Scaling Phenomena

As all biological networks tend to evolve over time, an architectural form that maximises flow under the constraints specific to it,6 it follows that similar scaling effects may also be demonstrated in the networks of urban systems, cities and conurbations. It is argued that as these patterns are also insensitive to topography and climate, it is likely that they are related to the flow and distribution of resources through ecological and urban networks.15
Figure 2. Networks for information distribution exhibit many similar parameters to the hierarchical branching metabolic networks of living forms, and a great variety of other culturally produced networks also exhibit comparable ‘scale free’ power law characteristics. Both biological and cultural networks grow continuously by the addition of new nodes or hubs, but these new nodes preferentially attach to nodes that are already well connected. Although there is wide variation in their individual components and chemical processes, the metabolic branching networks of all living forms, from the smallest of microbes to the very largest blue whale, exhibit the same topological scaling properties. Analysis of the large multi­decade data sets of mature Western cities reveals the space per person decreases as the population size increases; with greater densities and greater flows through transport infrastructures, there is a greater diversity of economic and cultural activities and the pace of all activities increases accordingly, including individual consumption and waste, crimes, pollution and diseases. The common metabolic characteristics are exhibited in the relations between the geometry and overall size of the body plan, the internal operating temperature and the mode of existence in the environment. Biological metabolism operates through surfaces and branching networks that exhibit identical mathematical parameters in all living forms, from the smallest microbes to giant sequoias, from mice to mammoths. Aerial view at night of south Mumbai
The night image indicates the vehicle flow and energy use of one developed patch of a city that has a population that has doubled in only 20 years and now exceeds 20 million people. In all living beings, the morphology of the species and their metabolism are intricately linked through the flow of energy and materials. There is also dramatically reduced access to open green spaces in high-density cities that correlates to city area more strongly than to population size; and in Europe to geographical location, in that green space per person increases proportionally with latitude, being greater in the northern latitudes than in southern-latitude cities.13
Scaling laws are exhibited by the distribution patterns found in many natural and cultural systems, and are considered fundamental to statistical physics. Higher levels of biological organisation emerge from metabolic processes, in the relations between species, and in the density and patterns of distribution of species across the surface of the earth.5
El! For example, just as the cardiovascular network distributes energy and materials to cells in a living form, so it seems that urban traffic networks distribute energy, materials and people through a city.7 Biological metabolism functions through surfaces and branching networks, and there has been a century or more of research into the mathematical parameters
common to all living forms. The extremely rapid growth is producing fragments of dense metropolitan development amongst extremely compromised urban environments and severe water shortages. The scaling is simply expressed as a power law: Y = Y0M where Y is an observable magnitude, Y0 a constant, and M is the mass of the organism. The linguist George Kingsley Zipf gave his name to the mathematical law that accounts for the frequency of occurrence of words within written texts14 and is observed in the rank size distributions of the largest cities and metropolises of the world, and metropolitan areas of the US, which seem to be robust over time despite multiple economic and social fluctuations and perturbations. The metabolic exponent b =3/4 is found across nearly 27 orders of magnitude in life, from molecular levels up to the largest organisms,9 in the differing metabolisms of ectotherms and endotherms,10 and in the photosynthetic metabolisms of plants.11
Scaling phenomena are also evident in cities,12 significantly in relation to the number of inhabitants rather than to the material mass of the built fabric.

Updated: 31.10.2014 — 06:21