neighborhood: Compute Neighborhood Structures of Specified Order

Description

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

Usage

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?

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.

Details

The adjacency matrix associated with the $i$th 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.

Examples

Run this code

#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))