Defining urban and regional phenomena in spatial terms of riddled with difficulties. The ecological fallacy has been known for 75 years or more, but recently the problem has emerged again in the debate concerning how cities perform economically as they get bigger. It has been supposed and sometimes demonstrated that as cities get bigger, some indicators such as income, patents, crime, and inequality scale super-linearly with size, suggesting that cities are more productive and innovative the larger they are but also are more hostile and unfair in their distribution of wealth and comparative advantage. In Britain, we have found however that cities do not grow in terms of their wealth as they get bigger. London of course does as it is a massive outlier but all the other cities simply scale in proportion to their size. This of course begs the question as whether or not Britain is an outlier when it comes to these kinds of agglomeration economies or whether or not it is because the urban system is much more highly integrated than other systems of cities. We assume the latter. To explore these ideas, we use percolation theory to define the boundaries of cities, starting from the giant cluster formed by the street network for England, Wales and Scotland and then thresholding this at different levels to produce a unique decomposition in terms of connectivity. The data is very fine scale with street intersections at a resolution of 100 metres or less and thus our analysis produces a hierarchical clustering the British space from 5km down to 50m. When we do this we not only define cities but also the nations that compose Britain, its regions, and then its cities. There are some very surprising results of doing this for historically the relative independence of Scotland immediately emerges, the deeply rooted north-south divide, the Welsh periphery, the southern Cornish Peninsula, Lincolnshire and the Wash, all places with their own identities.
Elsa Arcaute, Carlos Molinero, Erez Hatna, Roberto Murcio, Camilo Vargas-Ruiz, Paolo Masucci, Michael Batty (2015) Regions and Cities in Britain through hierarchical percolation,