rng: 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)

Arguments

a data matrix. Either x or dx must be provided.

an interpoint distance matrix.

a multiplier to grow the balls.

the value of p in the $L_p$ distance.

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.

Value

an object of class igraph, with the additional attributes
layoutthe x matrix.
r,parguments given to rng.

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 r times this distance if 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.

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.

Examples

Run this code

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

g <- rng(x)
plot(g)

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