1. Mapping Networks Or, the costs and benefits of abstraction

2. Mapping Networks What are Networks Elements of Network Mapping Schematic Maps

3. Networks, Defined What is a network?

4. 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

5. Elements of Networks Networks are a collection of: Nodes AKA: Vertices Edges AKA: Links

6. Early Quantitative Geography The Seven Bridges of Königsberg Famous network problem based on an actual place (An urban riddle) Let’s try and solve the riddle…

7. 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?

11. The problem becomes simpler with abstraction….

12. So, what’s 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)

13. 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

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

15. Beck’s Original

19. Direct descendents

21. The “Tube Map” Network Map of the London Underground A Schematic Diagram More Topological than Geographic

22. Tube Map Emphasizes connectivity over geographic congruence How?

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

24. 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…

27. Dangers of the schematic style What are the dangers of the beck map?

28. 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

29. Roman place-to-place maps

30. Peutinger’s Table

31. Speaking of routes……

32. 1643 Matthew Simons in A Direction for the English Traviller pub. Thomas Jenner (distance tables by John Norden)

33. Santa Fe Trail Zebulon Pike Map of the "Santa Fe Trail" St. Louis: ca. 1806 Manuscript map National Archives, Washington, D.C.

34. First map of the Arpanet

35. Map of the Internet

36. Conclusion “Graphs” are useful to simplify geographic spaces Sacrifices are made to achieve increased clarity