mapping networks

Mapping Networks

Or, the costs and benefits of abstraction

Mapping Networks

What are Networks

Elements of Network Mapping

Schematic Maps

Networks, Defined

What is a network?

Networks, Defined

What is a network?An interconnected group or systema system of intersecting lines or channels;

"a railroad network"; "a network of canals”

Networks are important in geography and mapping

Elements of Networks

Networks are a collection of:Nodes

AKA: Vertices

Edges AKA: Links

Early Quantitative Geography

The Seven Bridges of KönigsbergFamous network problem based on an

actual place (An urban riddle)Let’s try and solve the riddle…

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?

Is it possible to walk a route that crosses each bridge exactly once?

Is it possible to walk a route that crosses each bridge exactly once?

Is it possible to walk a route that crosses each bridge exactly once?

The problem becomes simpler with abstraction….

So, what’s the solution?

There is no solution! It is impossible.In 1736, Leonhard Euler proved it

impossibleFormulated solution in terms of “graph

theory” Eliminated all features except land masses

and the bridges (nodes, edges)

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

Harry Beck

Electrical Draftsman, English, 1903-1974

Created the most famous network map of all-time

What is it?

Beck’s Original

Direct descendents

The “Tube Map”

Network Map of the London Underground

A Schematic Diagram

More Topological than Geographic

Tube Map

Emphasizes connectivity over geographic congruence

How?

Octilinearity

Every line on the map is drawn in one of 8 directionsMultiples of 45 degreesOctilinearityReduces geographic congruence,

increases clarity

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…

Dangers of the schematic style

What are the dangers of the beck map?

Dangers of the schematic style

What are the dangers of the beck map?

Result in warped mental maps of actual geographySince distance and direction are inaccurate

Roman place-to-place maps

Peutinger’s Table

Speaking of routes……

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

Santa Fe Trail

Zebulon PikeMap of the "Santa Fe Trail"St. Louis: ca. 1806Manuscript mapNational Archives, Washington, D.C.

First map of the Arpanet

Map of the Internet

Conclusion

“Graphs” are useful to simplify geographic spaces

Sacrifices are made to achieve increased clarity