Proximity modeling, for our purposes here, will be taken as more or
less synonymous with graph embedding. A graph is a
mathematically defined object. The definition of a particular graph
includes two types of constituent objects. These are called
vertices and edges. Graphs have this nomenclature in
common with polyhedra (which also possess faces). When
envisioning graphs, it may do to imagine the vertices as dots, or
points; and the edges as line segments. Each edge has two ends, and
each end is attached to one of the graph's vertices. With graphs,
unlike with polyhedra, there is no general assumption that these lines
are "straight." The important thing about graphs is the question of
"what connects to what." For this reason, graph theory has found
applications in practices that have to do with connectivity, such as
electrical schematics and utility grids.
For the purpose of this discussion, the embedding of graphs will be taken to mean the drawing of graphs in (typically) two- or three-dimensional format, with a "goal" of keeping the edges as short as possible.
The pubwan literature includes many references to proximity modeling because it is seen as a way to position <a href="http://geocities.com/n8chz/pvo.htm">pubwan virtual objects</a> in virtual space. This is seen as a worthwhile endeavour because the exploration of conceivable arrangements of economic goods in "space" is seen as a possible fruitful area for knowledge discovery.
This site includes some public domain LISP code for exploring graph embedding. These routines are strictly "brute force" and should not be regarded as representing current knowledge about graph embedding or proximity modeling.
If you decide to load them into your favorite Common Lisp environment, make sure you have both files, and read the comments in order to understand the data structure used to represent a graph. You can get
these files at the following locations:
- http://geocities.com/n8chz/utgraph.txt
- http://geocities.com/n8chz/tweak.txt </o L> The above have been superseded by: http://geocities.com/n8chz/utgraph2.txt The search continues for more elegant and/or effective solutions, as well as a "front end" to interface with a pubwan database or interactive data entry (see volunteer information).