Gromov Hyperbolicity Constant

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Description

Computes the Gromov Hyperbolicity Constant of a distance matrix.

Usage

1

Arguments

d

A distance matrix of type dist or matrix, or anything that can be coerced into dist by as.dist. Must have at least 4 points.

deltas

A logical value specifying whether to return the vector of delta values. Default is FALSE.

scale

Specifies a scaling method for each delta. Default is no scaling (NA or "none"). Available methods are "max" which scales deltas by the max of the sums computed, and "perimeter" for the largest perimeter of the four points.

Details

This computes a constant that represents the relaxation of a 4-point condition for delta-hyperbolicity. See (Gromov 1987) for details.

Value

The Gromov hyperbolicity constant of the given distance matrix.

Author(s)

John Chakerian <chakj@stanford.edu>

References

M. Gromov. Hyperbolic groups. In Essays in Group Theory, pages 73-263. Springer, New York, 1987.

Chakerian, J. and Holmes, S. P. Computational Tools for Evaluating Phylogenetic and Heirarchical Clustering Trees. arXiv:1006.1015v1.

See Also

dist.multiPhylo

Examples

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# scale final delta by max distance
points <- cbind(runif(100), runif(100))
d <- dist(points)
gromov.hyperbolicity(d)/max(d)

# scale each delta by max distance for the 4 points
points <- cbind(runif(100), runif(100))
d <- dist(points)
gromov.hyperbolicity(d, scale="max")

# scale each delta by the max perimeter for the 4 points
points <- cbind(runif(100), runif(100))
d <- dist(points)
gromov.hyperbolicity(d, scale="max")