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Encyclopedia of GIS pp 409–413Cite as

Graph Theory, Konigsberg Problem

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Synonyms

Problem of seven bridges of Konigsberg; Euler's Konigsberg's bridges problem; Edge routing problems

Definition

In Geographic Information Systems, concepts from graph theory are extremely useful in expressing the spatial structure of entities seen as points, lines, areas and solids, after the geometrical details of these entities are removed. For example, in transportation and river networks, the topological properties of their structures can be represented using graphs. This article describes the origins of graph theory and the impact it has on various fields ranging from geography to economics.

The Konigsberg Bridge Problem is a classic problem, based on the topography of the city of Konigsberg, formerly in Germany but now known as Kalingrad and part of Russia. The river Pregel divides the city into two islands and two banks as shown in Fig 1. The city had seven bridges connecting the mainland and the islands (represented by thick lines in the figure). [1,2,3,4]. The problem...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Minnesota, Minneapolis, MN, USA

    Betsy George

Authors
  1. Betsy George
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Shashi Shekhar (McKnight Distinguished University Professor) (McKnight Distinguished University Professor)

  2. Management Science and Information Systems Department, Rutgers Business School Newark and New Brunswick Rutgers, the State University of New Jersey, Newark, NJ, 07102, USA

    Hui Xiong (Assistant Professor) (Assistant Professor)

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© 2008 Springer-Verlag

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George, B. (2008). Graph Theory, Konigsberg Problem. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_547

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