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We have observed that circles have been widely used in the literature to illustrate network results. There is at least one formal argument which helps us to understand why. If the elements of a set of nodes are equally spaced onto a circle, the sum of distances from each node to all other nodes is equal.

This seems to be a particularly favorable way to illustrate connections in a network. It allows even naive observers to perceive the contrast between a specific solution an the idealized pattern from which it deviates. (as an easily perceivable null hypothesis). This would also mean that other shapes could be used for specific problems as long as they offer regularity, like triangles or squares.

Constraining the possible solution to a set of locations being a member of a specific shape specifies at the same time a distance matrix between all permissible positions of the model.

If is the number of available positions in the solution space, the simple model can be described by the distances between all permissible positions, a matrix .

Lothar Krempel
Fri Mar 31 13:14:02 MET DST 1995