Structure, entropy and evolution of systems of cities

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Abstract

One of the main questions in Urban Science is whether systems of cities around the world show similarities in their structure and trajectories of development. Shannon entropy has played a crucial role in this line of research, both because it is a versatile measure of uniformity and because of its ability to discriminate significant patterns from only seemingly organised maximum randomness.
In this thesis, we present novel ways to analyse the structure of systems of cities and its evolution using entropy-based measures. We focus on key morphological aspects of a system of cities: the distribution of city sizes, their spatial arrangement, the population density and land use of their surroundings, and their connectivity via transport infrastructure; which we reconnect to human activities via spatial interaction models.
We propose normalisation formulae for the first degree-based graph entropy that facilitate its interpretation as a measure of balance of the degree sequence of a network. We define a local entropy measure for raster data that quantifies the heterogeneity of a variable of interest in the surroundings of each cell. We define a measure of morphological polycentricity for historical systems of cities based on the entropy of the most likely potential interactions between the cities.
We apply our methods to analyse systems of cities in different parts of the world and moments in history. We study the evolution of the entropy of city sizes in the main European powers from 1300 to 1850; the local entropy of land use and population density in Italy, the British Isles, and South Asia from 1700 to modern day; and the spatial organisation and morphological polycentricity of English and Welsh towns in the 19th century, via the entropy of spatial networks informed by the emerging railway system. Finally, we model the spatial-temporal dynamics of geo-tagged Tweets in London, of the Hungarian social network iWiW, and of the network of literary imitations between medieval Occitan troubadours.

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