# neighborhood: Compute Neighborhood Structures of Specified Order In sna: Tools for Social Network Analysis

## Description

For a given graph, returns the specified neighborhood structure at the selected order(s).

## Usage

 ```1 2 3``` ```neighborhood(dat, order, neighborhood.type = c("in", "out", "total"), mode = "digraph", diag = FALSE, thresh = 0, return.all = FALSE, partial = TRUE) ```

## Arguments

 `dat` one or more graphs. `order` order of the neighborhood to extract. `neighborhood.type` neighborhood type to employ. `mode` `"digraph"` if `dat` is directed, otherwise `"graph"`. `diag` logical; do the diagonal entries of `dat` contain valid data? `thresh` dichotomization threshold to use for `dat`; edges whose values are greater than `thresh` are treated as present. `return.all` logical; return neighborhoods for all orders up to `order`? `partial` logical; return partial (rather than cumulative) neighborhoods?

## Details

The adjacency matrix associated with the ith order neighborhood is defined as the identity matrix for order 0, and otherwise depends on the type of neighborhood involved. For input graph G=(V,E), let the base relation, R, be given by the underlying graph of G (i.e., G U G^T) if total neighborhoods are sought, the transpose of G if incoming neighborhoods are sought, or G otherwise. The partial neighborhood structure of order i>0 on R is then defined to be the digraph on V whose edge set consists of the ordered pairs (j,k) having geodesic distance i in R. The corresponding cumulative neighborhood is formed by the ordered pairs having geodesic distance less than or equal to i in R.

Neighborhood structures are commonly used to parameterize various types of network autocorrelation models. They may also be used in the calculation of certain types of local structural indices; `gapply` provides an alternative function which can be used for this purpose.

## Value

An array or adjacency matrix containing the neighborhood structures (if `dat` is a single graph); if `dat` contains multiple graphs, then a list of such structures is returned.

## Author(s)

Carter T. Butts [email protected]

`gapply`, `nacf`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```#Draw a random graph g<-rgraph(10,tp=2/9) #Show the total partial out-neighborhoods neigh<-neighborhood(g,9,neighborhood.type="out",return.all=TRUE) par(mfrow=c(3,3)) for(i in 1:9) gplot(neigh[i,,],main=paste("Partial Neighborhood of Order",i)) #Show the total cumulative out-neighborhoods neigh<-neighborhood(g,9,neighborhood.type="out",return.all=TRUE, partial=FALSE) par(mfrow=c(3,3)) for(i in 1:9) gplot(neigh[i,,],main=paste("Cumulative Neighborhood of Order",i)) ```