graphneigh
Graph based spatial weights
Functions return a graph object containing a list with the vertex
coordinates and the to and from indices defining the edges. Some/all of these functions assume that the coordinates are not exactly regularly spaced. The helper
function graph2nb
converts a graph
object into a neighbour list. The plot functions plot the graph objects.
 Keywords
 spatial
Usage
gabrielneigh(coords, nnmult=3)
relativeneigh(coords, nnmult=3)
soi.graph(tri.nb, coords, quadsegs=10)
graph2nb(gob, row.names=NULL,sym=FALSE)
"plot"(x, show.points=FALSE, add=FALSE, linecol=par(col), ...)
"plot"(x, show.points=FALSE, add=FALSE, linecol=par(col),...)
Arguments
 coords
 matrix of region point coordinates
 nnmult
 scaling factor for memory allocation, default 3; if higher values are required, the function will exit with an error; example below thanks to Dan Putler
 tri.nb
 a neighbor list created from tri2nb
 quadsegs
 number of line segments making a quarter circle buffer, see
gBuffer
 gob
 a graph object created from any of the graph funtions
 row.names
 character vector of region ids to be added to the
neighbours list as attribute
region.id
, defaultseq(1, nrow(x))
 sym
 a logical argument indicating whether or not neighbors should be symetric (if i>j then j>i)
 x
 object to be plotted
 show.points
 (logical) add points to plot
 add
 (logical) add to existing plot
 linecol
 edge plotting colour
 ...
 further graphical parameters as in
par(..)
Details
The graph functions produce graphs on a 2d point set that
are all subgraphs of the Delaunay triangulation. The relative neighbor graph is defined by the relation, x and y are neighbors if
$$d(x,y) \le min(max(d(x,z),d(y,z)) z \in S)$$
where d() is the distance, S is the set of points and z is an arbitrary point in S. The Gabriel graph is a subgraph of the delaunay triangulation and has the relative neighbor graph as a subgraph. The relative neighbor graph is defined by the relation x and y are Gabriel neighbors if
$$d(x,y) \le min((d(x,z)^2 + d(y,z)^2)^{1/2} z \in S)$$
where x,y,z and S are as before. The sphere of influence graph is
defined for a finite point set S, let $r_x$ be the distance from point x
to its nearest neighbor in S, and $C_x$ is the circle centered on x. Then
x and y are SOI neigbors iff $C_x$ and $C_y$ intersect in at
least 2 places. From 20160531, Computational Geometry in C code replaced by calls to functions in RANN and rgeos; with a large quadsegs=
argument, the behaviour of the function is the same, otherwise buffer intersections only closely approximate the original function.
See card
for details of “nb” objects.
Value

A list of class
Graph
withte following elementsThe helper functions return an nb
object with a list of integer
vectors containing neighbour region number ids.
References
Matula, D. W. and Sokal R. R. 1980, Properties of Gabriel graphs relevant to geographic variation research and the clustering of points in the plane, Geographic Analysis, 12(3), pp. 205222.
Toussaint, G. T. 1980, The relative neighborhood graph of a finite planar set, Pattern Recognition, 12(4), pp. 261268.
Kirkpatrick, D. G. and Radke, J. D. 1985, A framework for computational morphology. In Computational Geometry, Ed. G. T. Toussaint, North Holland.
See Also
Examples
example(columbus)
coords < coordinates(columbus)
par(mfrow=c(2,2))
col.tri.nb<tri2nb(coords)
col.gab.nb<graph2nb(gabrielneigh(coords), sym=TRUE)
col.rel.nb< graph2nb(relativeneigh(coords), sym=TRUE)
plot(columbus, border="grey")
plot(col.tri.nb,coords,add=TRUE)
title(main="Delaunay Triangulation")
plot(columbus, border="grey")
plot(col.gab.nb, coords, add=TRUE)
title(main="Gabriel Graph")
plot(columbus, border="grey")
plot(col.rel.nb, coords, add=TRUE)
title(main="Relative Neighbor Graph")
plot(columbus, border="grey")
if (require(rgeos, quietly=TRUE) && require(RANN, quietly=TRUE)) {
col.soi.nb< graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)
plot(col.soi.nb, coords, add=TRUE)
title(main="Sphere of Influence Graph")
}
par(mfrow=c(1,1))
dx < rep(0.25*0:4,5)
dy < c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5))
m < cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy))
try(res < gabrielneigh(m))
res < gabrielneigh(m, nnmult=4)
summary(graph2nb(res))
grd < as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data
r2 < gabrielneigh(grd)
set.seed(1)
grd1 < as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25)
r3 < gabrielneigh(grd1)
opar < par(mfrow=c(1,2))
plot(r2, show=TRUE, linecol=2)
plot(r3, show=TRUE, linecol=2)
par(opar)