\name{rng}
\alias{rng}
%- Also NEED an `\alias' for EACH other topic documented here.
\title{ Relative Neighborhood Graph.}
\description{
   the relative neighborhood graph defined by a set of points.
}
\usage{
rng(x=NULL, dx=NULL, r = 1, p = 2, usedeldir=TRUE)
}
%- maybe also `usage' for other objects documented here.
\arguments{
  \item{x}{ a data matrix. Either \code{x} or \code{dx} must be provided.}
  \item{dx}{ an interpoint distance matrix.}
  \item{r}{ a multiplier to grow the balls.}
  \item{p}{ the value of p in the \eqn{L_p} distance.}
  \item{usedeldir}{a logical. If true and the data are two dimensional
        and the deldir package is installed, the Delaunay triangularization
		  is first computed, and this is used to compute the relative
		  neighborhood graph.}
}
\details{
   the relative neighborhood graph is defined in terms of balls
	centered at observations. For two observations, the balls are
	set to have radius equal to the distance between the observations
	(or \code{r} times this distance if \code{r} is not 1). There is
	an edge between the vertices associated with the observations if 
	and only if there are no vertices in the lune defined by the
	intersection of the balls.
}
\value{
	an object of class igraph, with the additional attributes
   \item{layout}{the x matrix.}
	\item{r,p}{arguments given to \code{rng}.}
}
\references{ 

J.W. Jaromczyk and G.T. Toussaint,
"Relative neighborhood graphs and their relatives",
Proceedings of the IEEE, 
80, 1502-1517, 1992.

G.T. Toussaint,
"A Graph-Theoretic Primal Sketch",
Computational Morphology, 229-260, 1988.

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

}
\author{ David J. Marchette david.marchette@navy.mil}

\seealso{\code{\link{gg}},\code{\link{cccd}},\code{\link{ccd}}}

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

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

}
\keyword{ math }