The Mathematical Foundations of the Science of Cities

  • Christa BrelsfordEmail author
  • Taylor Martin
Living reference work entry


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.


Cities Graph theory Network science Social network analysis Infrastructure Urban planning Space syntax Urban scaling theory 


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Copyright information

© This is a U.S. Government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.Oak Ridge National LaboratoryOak RidgeUSA
  2. 2.Sam Houston State UniversityHuntsvilleUSA

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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