[R-sig-Geo] poly2nb neighbour itself should be considered a neighbour

[Elias T. Krainski]

Hello,

I found this matter easier when working with matrix representations. Set

  A^0 = I (identity matrix),

  A^1 = A, where A_{ij} = 1 if j is neighbor to j and zero otherwise 
(this consider A_{ii} = 0)

  A^2 = A'A

  A^3 = A'A^2 and so on

The A^k_{ij} entry gives _how many steps of length k there is between i 
and j_. To me, this definition makes this matter clear. See an example 
considering a 10x10 regular grid:

nb <- grid2nb(d=c(10,10), queen = FALSE)
nn <- card(nb)
A1 <- sparseMatrix(
  i = rep(1:length(nn), nn),
  j = unlist(nb[nn>0]), x=1)
A2 <- crossprod(A1)
image(A1)
image(A2)

best regards,

Elias

On 03/11/2019 17:46, Dexter Locke wrote:
> Dear Robert,
>
> It sounds like what you are looking for is typically called a second order neighbor. Higher order neighbors can also included in a weights matrix such as your neighbors’, neighbors’, neighbor which is a third-order neighbor. I think you are seeking second-order neighbors.
>
> See the spdep vignettes, and the section 5 Higher-Order Neighbors subsection here: https://cran.r-project.org/web/packages/spdep/vignettes/nb.pdf in particular. The spdep::nblag might be what you need, but without additional information it is hard to know.
>
> Good luck,
> Dexter
> dexterlocke.com
>
>
>
>> On Nov 3, 2019, at 2:12 PM, Robert R <usercatch using outlook.com> wrote:
>>
>> Dear All,
>>
>> I would like to know if the function "poly2nb" ("spdep" package.) let me create a neighborhood of itself, i.e., not only its queen neighbors (queen=TRUE), but a neighbour itself should also be considered a neighbour.
>>
>> I am looking to create a queen weight neighborhood matrix afterwards using "nb2listw".
>>
>> Any help would help me a lot.
>>
>> Many thanks
>>
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