# Unusual variance measure

I explore centrality measures for graphs and discretized regions.
The data array (for given point) is all distances from this point to the boundary of region.
At the beginning I used standard deviation of this array as measure of centrality of point
(the smaller deviation, the more centrality).
But recently I've found simple criterion (for strictly positive arrays): $$\kappa=\frac{\min(arr)}{\max(arr)}$$ This measure is very clear and illustrative:

I wonder if this measure is always used in statistics, what are its properties?

• Your example includes two regions with the same linear scale. You should see if this metric continues to make sense if the regions radially differ in scale. In particular, if the size of the region goes to zero, then the centrality by this metric will diverge.
– Dave
Commented Jan 2 at 17:48
• Though as far as I know not known/studied, this metric has some similarities to several cluster quality metrics like the Davies-Boulding index and the Dunn index
– Dave
Commented Jan 2 at 18:00

• The closest thing to it, that is quite popular is range, which just uses a different arithmetic operation, i.e. $$\max(arr) - \min(arr)$$.