Check Contiguity by Group

Identify contiguous sets of units and numbers each set. Can be extended to repeat the procedure within a subgeography.

check_contiguity(adj, group)

cct(adj, group)

ccm(adj, group)

Arguments

adj

adjacency list

group

array of group identifiers. Typically district numbers or county names. Defaults to 1 if no input is provided, checking that the adjacency list itself is one connected component.

Value

tibble with contiguity indicators. Each row is the units of adj. Columns include

• group Values of the inputted group argument. If group is not specified, then all values will be 1.

• component A number for each contiguous set of units within a group. If all units within a group are contiguous, all values are 1. If there are two sets, each discontiguous with the other, the larger one will be numbered 1 and the smaller one will be numbered as 2.

Details

Given a zero-indexed adjacency list and an array of group identifiers, this returns a tibble which identifies the connected components. The three columns are group for the inputted group, group_number which uniquely identifies each group as a positive integer, and component which identifies the connected component number for each corresponding entry of adjacency and group. If everything is connected within the group, then each element of component will be 1. Otherwise, the largest component is given the value 1, the next largest 2, and so on.

If nothing is provided to group, it will default to a vector of ones, checking if the adjacency graph is connected.

cct() is shorthand for creating a table of the component values. If everything is connected within each group, it returns a value of 1. In general, it returns a frequency table of components.

ccm() is shorthand for getting the maximum component value. It returns the maximum number of components that a group is broken into. This returns 1 if each group is connected. #'

Examples

data(checkerboard)
adj <- adjacency(checkerboard)
#> Warning: Planarizing skipped. `x` missing CRS.
# These each indicate the graph is connected.
check_contiguity(adj) # all contiguous
#> # A tibble: 64 × 3
#>    group group_number component
#>    <int>        <int>     <int>
#>  1     1            1         1
#>  2     1            1         1
#>  3     1            1         1
#>  4     1            1         1
#>  5     1            1         1
#>  6     1            1         1
#>  7     1            1         1
#>  8     1            1         1
#>  9     1            1         1
#> 10     1            1         1
#> # ℹ 54 more rows
# If there are two discontiguous groups, there will be 2 values of `component`
cct(adj)
#> 
#>  1 
#> 64 
ccm(adj)
#> [1] 1