Proximity modeling

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.

Proximity modeling is seen as a way to position virtual objects 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.

http://geocities.com/n8chz/utgraph2.txt