Abstract
In this chapter, we describe graph-theoretic representations of infrastructure and social processes in urban environments and trace the development of these fields from the perspective of mathematics, social science, and urban planning. We follow the historical development of two different perspectives on cities and urban planning – one in which infrastructure and urban form is the primary focus and another which made people and social processes the primary focus. These perspectives can be traced through their application of concurrently developing mathematical techniques in graph theory, network science, and social network analysis. These different perspectives are now becoming integrated into a more mathematically grounded understanding of cities as coupled social and physical systems, in which the social life of a city shapes and defines the infrastructure that is built and a city’s infrastructure and physical form also shape the lives and communities of its residents.
This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
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Brelsford, C., Martin, T. (2019). The Mathematical Foundations of the Science of Cities. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_56-1
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DOI: https://doi.org/10.1007/978-3-319-70658-0_56-1
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