Mapping Networks

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Mapping Networks

• Or, the costs and benefits of abstraction

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Mapping Networks

• What are Networks
• Elements of Network Mapping
• Schematic Maps

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Networks, Defined

• What is a network?

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Networks, Defined

• What is a network?
• An interconnected group or system
• a system of intersecting lines or channels "a
  railroad network" "a network of canals
• Networks are important in geography and mapping

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Elements of Networks

• Networks are a collection of
• Nodes
• AKA Vertices
• Edges
• AKA Links

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Early Quantitative Geography

• The Seven Bridges of Königsberg
• Famous network problem based on an actual place
  (An urban riddle)
• Lets try and solve the riddle

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• The city of Königsberg is set on the Pregel
  River.
• The city included 2 large islands and was
  connected to the mainland by exactly 7 large
  bridges
• Is it possible to walk a route that crosses each
  bridge exactly once?

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Is it possible to walk a route that crosses each
bridge exactly once?
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Is it possible to walk a route that crosses each
bridge exactly once?
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Is it possible to walk a route that crosses each
bridge exactly once?
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The problem becomes simpler with abstraction.
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So, whats the solution?

• There is no solution! It is impossible.
• In 1736, Leonhard Euler proved it impossible
• Formulated solution in terms of graph theory
• Eliminated all features except land masses and
  the bridges (nodes, edges)

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A Eulerian Path

• A solution did not exist
• Problem concerned degrees of nodes
• Degree of a node is the number of edges touching
  it
• Konisberg 1 5-degree node, 3 3-degree nodes
• Euler proved that a circuit is only possible
  if there are exactly 0 or 2 nodes of an odd
  degree
• This type of walk is called a Eulerian Path

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Harry Beck

• Electrical Draftsman, English, 1903-1974
• Created the most famous network map of all-time
• What is it?

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Becks Original
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Direct descendents
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The Tube Map

• Network Map of the London Underground
• A Schematic Diagram
• More Topological than Geographic

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Tube Map

• Emphasizes connectivity over geographic
  congruence
• How?

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Octilinearity

• Every line on the map is drawn in one of 8
  directions
• Multiples of 45 degrees
• Octilinearity
• Reduces geographic congruence, increases clarity

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The Beck Map

• First drafts made between 1931-1933
• Designed in the form of the electrical circuitry
  diagrams of that time
• Style adopted worldwide
• Subway maps are among the most used network maps

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Dangers of the schematic style

• What are the dangers of the beck map?

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Dangers of the schematic style

• What are the dangers of the beck map?
• Result in warped mental maps of actual geography
• Since distance and direction are inaccurate

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Roman place-to-place maps
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Peutingers Table
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Speaking of routes
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1643  Matthew Simons in A Direction for the
English Traviller pub. Thomas Jenner (distance
tables by John Norden)
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Santa Fe Trail
Zebulon PikeMap of the "Santa Fe Trail"St.
Louis ca. 1806Manuscript mapNational Archives,
Washington, D.C.
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First map of the Arpanet
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Map of the Internet
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Conclusion

• Graphs are useful to simplify geographic spaces
• Sacrifices are made to achieve increased clarity