graphneigh: Graph based spatial weights

In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description

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.

Usage

gabrielneigh(coords, nnmult=3)
relativeneigh(coords, nnmult=3)

soi.graph(tri.nb, coords, quadsegs=10)
graph2nb(gob, row.names=NULL,sym=FALSE)
## S3 method for class 'Gabriel'
plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...)
## S3 method for class 'relative'
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, default seq(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) <= 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 sub-graph. The relative neighbor graph is defined by the relation x and y are Gabriel neighbors if

d(x,y) <= 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 2016-05-31, 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 elements

np	number of input points
from	array of origin ids
to	array of destination ids
nedges	number of edges in graph
x	input x coordinates
y	input y coordinates

The helper functions return an nb object with a list of integer vectors containing neighbour region number ids.

Author(s)

Nicholas Lewin-Koh [e-mail]

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. 205-222.

Toussaint, G. T. 1980, The relative neighborhood graph of a finite planar set, Pattern Recognition, 12(4), pp. 261-268.

Kirkpatrick, D. G. and Radke, J. D. 1985, A framework for computational morphology. In Computational Geometry, Ed. G. T. Toussaint, North Holland.

See Also

knearneigh, dnearneigh, knn2nb, card

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)

Example output

Loading required package: sp
Loading required package: Matrix

colmbs> require(maptools)
Loading required package: maptools
Checking rgeos availability: TRUE

colmbs> columbus <- readShapePoly(system.file("etc/shapes/columbus.shp",
colmbs+  package="spdep")[1])

colmbs> col.gal.nb <- read.gal(system.file("etc/weights/columbus.gal",
colmbs+  package="spdep")[1])
Warning message:
use rgdal::readOGR or sf::st_read 

     PLEASE NOTE:  The components "delsgs" and "summary" of the
 object returned by deldir() are now DATA FRAMES rather than
 matrices (as they were prior to release 0.0-18).
 See help("deldir").
 
     PLEASE NOTE: The process that deldir() uses for determining
 duplicated points has changed from that used in version
 0.0-9 of this package (and previously). See help("deldir").


rgeos version: 0.3-23, (SVN revision 546)
 GEOS runtime version: 3.4.2-CAPI-1.8.2 r3921 
 Linking to sp version: 1.2-3 
 Polygon checking: TRUE 

Error in gabrielneigh(m) : number of neighbours overrun - increase nnmult
Neighbour list object:
Number of regions: 100 
Number of nonzero links: 342 
Percentage nonzero weights: 3.42 
Average number of links: 3.42 
1 region with no links:
100
Non-symmetric neighbours list
Link number distribution:

 0  1  2  3  4  5 
 1  8 10 18 55  8 
8 least connected regions:
46 47 48 49 96 97 98 99 with 1 link
8 most connected regions:
10 15 20 25 30 35 40 45 with 5 links

spdep documentation built on Aug. 19, 2017, 3:01 a.m.