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.

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.

Here is 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://web.archive.org/20091027073504/geocities.com/n8chz/utgraph.txt
- http://geocities.com/n8chz/tweak.txt </o L>

The above have been superseded by:

http://web.archive.org/20091027073419/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 public domain database or

interactive data entry (see volunteer information).