\name{gg}
\alias{gg}
\title{ 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, method = NULL, usedeldir = TRUE, open = TRUE, 
   k = NA, algorithm = 'cover_tree')
}
\arguments{
  \item{x}{ a matrix of observations.}
  \item{r}{ a multiplier on the ball radius.}
  \item{method}{ the method used for the distance. 
     See \code{\link[proxy]{dist}}}
  \item{usedeldir}{logical. Whether to use the deldir package or not.}
  \item{open}{logical. If TRUE, open balls are used in the definition.}
  \item{k}{If given, \code{get.knn} is used from FNN to approximate
   the Gabriel graph. Only the \code{k} nearest neighbors to
	the points are used to determine whether an edge should be made or not.
	This will be much faster and use less memory for large data sets, but 
	is an approximation unless \code{k} is sufficiently large.}
  \item{algorithm}{See \code{\link[FNN]{get.knn}}.}
}
\details{
   places an edge between two points \eqn{i,j} if the ball centered between
	the points with radius \eqn{r d(i,j)/2} contains no other points.
}
\value{
  an object of class igraph. In addition it contains the attributes:
  \item{layout}{ the data.}
  \item{r,p}{arguments passed to \code{gg}}
}
\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.

}
\author{ David J. Marchette}

\seealso{ \code{\link{rng}}, \code{\link[proxy]{dist}}, \code{\link[FNN]{get.knn}}}

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

g <- gg(x)
\dontrun{
plot(g)
}

}
\keyword{ graphs }