Network Matrix Exercise

(http://faculty.washington.edu/krumme/350/exercises/network.html)

Please do NOT YET connect your network exercise page to your homepage. Please print it out, i.e. submit the assignment on paper (Neat + "professional", sharp pencil, please! The verbal part needs to be typed!). Be sure that you have complied with all component requirements. If you have created a Web page for this exercise (and you are encouraged to so) please identify the URL of your (not-connected) submission. Thanks!

Due: see Calendar!

Supporting Resources:

• Network Structures & Measures
• Matrix Multiplications
• Taaffe & Gauthier readings (see below or class agenda)
• Taaffe & Gauthier Example
• Your class notes

                    B             D
                   /\            /
                  /  \          /
                 /    \        /
                /      \      /
               /        \    /
              /          \  /
             /____________\/
            A              C

Introduce directions into the graph ABCD so that you can reach B directly from A (C from B and A from C) , but not A from B (B from C, and C from A). Only the link CD remains two-directional.

1. What is the new diameter? Why do we need it for the determination of the accessibility matrix?
2. Derive the (final) "accessibility matrix" for this new (now "directed") graph. [All calculations should be made explicit, i.e. step-by-step]
3. Characterize, in detail (at least three sentences), the locational change (change in accessibility) of the individual nodes (stress the "forward" and "backward" distinction between linkages). Do not hesitate to use an example for these directed interdependencies.
4. WITHOUT calculating another final accessibility matrix, describe the effects of the following two changes in the network namely
   1. the (directed) extension of the route C_D to a new node E; and .
   2. the addition of a new directional route from E to A.
   on
   1. the calculation of the accessibility matrix and
   2. the accessibility characteristics of the old nodes.

You are encouraged to use resources for both, calculations and your interpretation, including class handouts and Gauthier & Taaffe, Geography of Transportation, chapters on structural analysis of networks (ch.5 of the 1973 edition).