I have a handful of N "things" for which I have a NxN symmetric correlation matrix. The correlations are a based on a custom scheme for quantifying similarity between complex things, with a value range 0% to 100%, though the values for the N things are all high (95.4%-97.4%). I want to visualize the similarities and differences using force directed graph visualization .
I was going to use 1 minus the correlations as a distance metric. Is this an appropriate for correlations, particularly when values are all high?
Googling hasn't been my friend when searching for the intersection between correlation matrices and graph visualization. My thought is that 1 minus the correlation plots the N things with distances somewhat proportional to their very small differences. An alternative might be to use the reciprocal of the correlation as the distance, but since the values are close to one, the Taylor expansion would show such a distance would be similar to 1 minus the correlation. The two schemes would differ much more for near-zero correlations, where the reciprocal would yield a distance approaching infinity (not practical for graph visualization). I can tweak the 1 minus distance scheme by raising to various powers, greater or less than 1 depending on whether I want to emphasize the small distances or the great distances.
 I would be using Matlab's
layout tool, which uses Fruchterman & Reingold's "Graph Drawing by Force-directed Placement." Software — Practice & Experience. Vol. 21 (11), 1991, pp. 1129–1164.