cccd (version 1.00.05)

gg: Gabriel Graph

Description

A Gabriel graph is one where the vertices are points and there is an edge between two points if the maximal ball between the points contains no other points.

Usage

gg(x, r = 1, p = 2, usedeldir = TRUE)

Arguments

x

a matrix of observations.

r

a multiplier on the ball radius.

p

the value of p in the $L_p$ distance.

usedeldir

logical. Whether to use the deldir package or not.

Value

• an object of class igraph. In addition it contains the attributes:
• layout
  the data.
• r,p
  arguments passed to gg

Details

places an edge between two points $i,j$ if the ball centered between the points with radius $r d(i,j)/2$ contains no other points.

References

K.R. Gabriel and R.R. Sokal, A New Statistical Approach to Geographic Variation Analysis, Systemic Zoology, 18, 259-278, 1969

D.J. Marchette, Random Graphs for Statistical Pattern Recognition, John Wiley & Sons, 2004.

See Also

rng

Examples

x <- matrix(runif(100),ncol=2)

g <- gg(x)
plot(g)