ade4 (version 1.7-22)

neig: Neighbourhood Graphs

Description

neig creates objects of class neig with :
a list of edges
a binary square matrix
a list of vectors of neighbours
an integer (linear and circular graphs)
a data frame of polygons (area)

scores.neig returns the eigenvectors of neighbouring,
orthonormalized scores (null average, unit variance 1/n and null covariances) of maximal autocorrelation.

nb2neig returns an object of class neig using an object of class nb in the library 'spdep'

neig2nb returns an object of class nb using an object of class neig

neig2mat returns the incidence matrix between edges (1 = neighbour ; 0 = no neighbour)

neig.util.GtoL and neig.util.LtoG are utilities.

Usage

neig(list = NULL, mat01 = NULL, edges = NULL,
    n.line = NULL, n.circle = NULL, area = NULL)
scores.neig  (obj) 
# S3 method for neig
print(x, ...) 
# S3 method for neig
summary(object, ...)
nb2neig (nb)
neig2nb (neig)
neig2mat (neig)

Arguments

list

a list which each component gives the number of neighbours

mat01

a symmetric square matrix of 0-1 values

edges

a matrix of 2 columns with integer values giving a list of edges

n.line

the number of points for a linear plot

n.circle

the number of points for a circular plot

area

a data frame containing a polygon set (see area.plot)

nb

an object of class 'nb'

neig, x, obj, object

an object of class 'neig'

...

further arguments passed to or from other methods

Author

Daniel Chessel

References

Thioulouse, J., D. Chessel, and S. Champely. 1995. Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1--14.

Examples

if(!adegraphicsLoaded()) {
  
  if(requireNamespace("deldir", quietly = TRUE)) {
  
    data(mafragh)
    par(mfrow = c(2, 1))
    provi <- deldir::deldir(mafragh$xy)
    provi.neig <- neig(edges = as.matrix(provi$delsgs[, 5:6]))
    
    s.label(mafragh$xy, neig = provi.neig, inc = FALSE, 
      addax = FALSE, clab = 0, cnei = 2)
    dist <- apply(provi.neig, 1, function(x) 
      sqrt(sum((mafragh$xy[x[1], ] - mafragh$xy[x[2], ]) ^ 2)))
    #hist(dist, nclass = 50)
    mafragh.neig <- neig(edges = provi.neig[dist < 50, ])
    s.label(mafragh$xy, neig = mafragh.neig, inc = FALSE, 
      addax = FALSE, clab = 0, cnei = 2)
    par(mfrow = c(1, 1))
    
    data(irishdata)
    irish.neig <- neig(area = irishdata$area)
    summary(irish.neig)
    print(irish.neig)
    s.label(irishdata$xy, neig = irish.neig, cneig = 3,
      area = irishdata$area, clab = 0.8, inc = FALSE)
    
    irish.scores <- scores.neig(irish.neig)
    par(mfrow = c(2, 3))
    for(i in 1:6)
      s.value(irishdata$xy, irish.scores[, i], inc = FALSE, grid = FALSE, addax = FALSE,
        neig = irish.neig, csi = 2, cleg = 0, sub = paste("Eigenvector ",i), csub = 2)
    par(mfrow = c(1, 1))
    
    a.neig <- neig(n.circle = 16)
    a.scores <- scores.neig(a.neig)
    xy <- cbind.data.frame(cos((1:16) * pi / 8), sin((1:16) * pi / 8))
    par(mfrow = c(4, 4))
    for(i in 1:15)
      s.value(xy, a.scores[, i], neig = a.neig, csi = 3, cleg = 0)
    par(mfrow = c(1, 1))
    
    a.neig <- neig(n.line = 28)
    a.scores <- scores.neig(a.neig)
    par(mfrow = c(7, 4))
    par(mar = c(1.1, 2.1, 0.1, 0.1))
    for(i in 1:27)
      barplot(a.scores[, i], col = grey(0.8))
    par(mfrow = c(1, 1))
  }

  if(requireNamespace("spdep", quietly = TRUE)) {
    
    data(mafragh)
    maf.rel <- spdep::relativeneigh(as.matrix(mafragh$xy))
    maf.rel <- spdep::graph2nb(maf.rel)
    s.label(mafragh$xy, neig = neig(list = maf.rel), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2)
    
    par(mfrow = c(2, 2))
    w <- matrix(runif(100), 50, 2)
    x.gab <- spdep::gabrielneigh(w)
    x.gab <- spdep::graph2nb(x.gab)
    s.label(data.frame(w), neig = neig(list = x.gab), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "relative")
    x.rel <- spdep::relativeneigh(w)
    x.rel <- spdep::graph2nb(x.rel)
    s.label(data.frame(w), neig = neig(list = x.rel), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "Gabriel")
    k1 <- spdep::knn2nb(spdep::knearneigh(w))
    s.label(data.frame(w), neig = neig(list = k1), inc = FALSE,
      clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "k nearest neighbours")
    
    all.linked <- max(unlist(spdep::nbdists(k1, w)))
    z <- spdep::dnearneigh(w, 0, all.linked)
    s.label(data.frame(w), neig = neig(list = z), inc = FALSE, clab = 0, 
      addax = FALSE, cne = 1, cpo = 2, sub = "Neighbourhood contiguity by distance")
    par(mfrow = c(1, 1))
  }
  
}