Graphy Theory: Tesseract Representation
- To: mathgroup at smc.vnet.net
- Subject: [mg22842] Graphy Theory: Tesseract Representation
- From: "David Kazmer" <kazmer at ecs.umass.edu>
- Date: Sat, 1 Apr 2000 02:51:04 -0500 (EST)
- Organization: College of Engineering, University of Massachusetts
- Sender: owner-wri-mathgroup at wolfram.com
Here's a potentially interesting problem. I wish to represent a Tesseract, a 4D cube with +/-1 vertices, as a 2D graph. This graph also represents a full factorial design of experiments (my interest). In the desired graph, the first column represents the 16 permutations corresponding to 4D coordinates. The subsequent four columns represent each of the four coordinates, with each of the two rows representing the -1 and +1 levels of those states. Edges connect the elements of the permutation to the four dimensions. I know how to do it, but there is a question of efficiency. You could: 1. Construct CompleteGraph[16, 2, 2, 2, 2], then 2. Remove edges using exhaustive edge checks. I believe that this graph could be constructed very easily in Mathematica. Any ideas? Also, is anyone aware of this type of graph being prevalent in any domain? It has some interesting uses. Best wishes, dave.