Figure 2.9 A range of spatial weights applied to polygon data

figures

code

This figure is intended to demonstrate the diversity of possible conceptualisations of ‘neighbour’ that are often deployed in spatial analysis contexts, and represent possible different approaches to relative space.

The spdep package I am using here is not the easiest to use. The best guidance on spdep I’ve found is in

Bivand R, EJ Pebesma, and V Gómez-Rubio. 2013. Applied Spatial Data Analysis with R. 2nd edn. Springer.

The newer sfdep package is still finding its feet at time of writing (Oct 2023), but will likely be a better choice before long.

Code

library(sf)
library(dplyr)
library(spdep)
library(sp)

Assembling the data

First read a polygons dataset. You’ll need to supply your own for this.

Code

chch <- st_read("chch-sa2.gpkg") # you need a spatial dataset

spdep requires the data to be in the sp package format, so we convert to that.

Code

polys <- chch |>
  select(geom) |>
  as("Spatial")

Now make some points inside the polygons, and also some centroids.

Code

# guaranteed inside the polygons
pts <- chch |>
  st_point_on_surface() |> 
  st_geometry()

# not guaranteed, but better(?) for distance measurements
pts_c <- chch |>
  st_centroid() |> 
  st_geometry()

Maps of adjacencies based on different rules

These are presented in a single figure in the book in four rows of three. Here I show them as sets of three for greater clarity.

Contiguity based

Code

layout(matrix(1:3, ncol = 3, byrow = TRUE))
par(mai = c(0, 0, 0.15, 0))

nb <- polys |> poly2nb(queen = TRUE)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Queen's rule adjacency")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- polys |> poly2nb(queen = FALSE)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Rook's rule adjacency")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- nb |> nblag(2) |> nblag_cumul()
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Cumulative lag-2 adjacency")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

k-nearest neighbours

Note that we use the centroids (pts_c) to calculate the distances, but the points inside the polygons (pts) from st_point_on_surface() for the plotting.

Code

layout(matrix(1:3, ncol = 3, byrow = TRUE))
par(mai = c(0, 0, 0.15, 0))

nb <- pts_c |> knearneigh(k = 3) |> knn2nb()
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "k = 3")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- pts_c |> knearneigh(k = 6) |> knn2nb()
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "k = 6")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- pts_c |> knearneigh(k = 12) |> knn2nb()
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "k = 12")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

Distance criteria

Next, distance criteria, again calculated from centroids, but visualised using the st_point_on_surface().

Code

layout(matrix(1:3, ncol = 3, byrow = TRUE))
par(mai = c(0, 0, 0.15, 0))

nb <- pts_c |> dnearneigh(d1 = 0, d2 = 1000)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Distance < 1000")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- pts_c |> dnearneigh(d1 = 0, d2 = 1500)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Distance < 1500")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

nb <- pts_c |> dnearneigh(d1 = 1500, d2 = 2000)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "1500 < Distance < 2000")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

Graph-based approaches

Finally, some network-based possibilities, Delaunay triangulation, Gabriel graph and the relative neighbour graph.

Code

layout(matrix(1:3, ncol = 3, byrow = TRUE))
par(mai = c(0, 0, 0.15, 0))

g <- tri2nb(pts_c)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Delaunay triangulation")
plot(g, pts, col = 'red', lwd = 0.5, add = TRUE)

g <- gabrielneigh(pts_c)
nb <- graph2nb(g)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Gabriel graph")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

g <- relativeneigh(pts_c)
nb <- graph2nb(g)
plot(polys, col = "lightgrey", lwd = 0.5, border = 'white', 
     main = "Relative neighbour graph")
plot(nb, pts, col = 'red', lwd = 0.5, add = TRUE)

Code

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