csg: Construct connected subgraphs

In jpfrench81/smerc: Statistical Methods for Regional Counts

Construct connected subgraphs

Description

csg2, lcsg2, and scsg2 construct connected subgraphs. These functions are not intended for users. nn contains a list of nearest neighbors for each region. idx is a vector of possible vertices being considered as a subgraph. w is a connectivity matrix relating the N vertices. w[i,j] = 1 if vertices i and j are connected, i.e., if they share an edge. The dimensions of w are N times k, where k = length(idx). While the rows of w contain adjacency information for all N vertices, only the idx columns of the complete adjacency matrix are used in w. See Details for discussion of scsg.

Usage

csg2(cz, cnn, cw)

lcsg2(lcz, cnn, cw)

scsg2(
  nn,
  w,
  idx = seq_along(nn),
  nlevel = NULL,
  verbose = FALSE,
  logical = FALSE
)

Arguments

cz	A logical vector representing the current subgraph.
cnn	The indices of the neighbors of the current vertex.
cw	A binary adjacency matrix for the neighbors of the current vertex.
lcz	A list of current zones (in the form of logical vectors).
nn	A list of the nearest neighbors for each vertex (region).
w	A binary adjacency matrix indicating connected neighbors.
idx	A vector of vertices for which to construct the set of connected subgraphs.
nlevel	The maximum size of each subgraph.
verbose	A logical value indicating whether descriptive messages should be provided. Default is FALSE. If TRUE, this can be useful for diagnosing where the sequences of connected subgraphs is slowing down/having problems.
logical	A logical value indicating whether a list of logical vectors should be returned. The default is FALSE, indicating that the scsg function should return a list of vectors with each vector containing the vertex indices included in each subgraph.

Details

scsg2 performs a sequence of lcsg2 calls. Starting with lcz == list(idx[1]), scsg keeps iteratively building more connected subsgraphs by perfoming something like: lcz1 = list(idx[1]). lcz2 = lcsg2(lcz1, ...). lcz3 = lcsg2(lcz2, ...). This is done until there are no more connected subgraphs among the elements of idx.

Value

A list with all possible connected subgraphs based on the user-provided parameters.

Examples

data(nydf)
data(nyw)
# determine 50 nn of region 1 for NY data
coords <- as.matrix(nydf[, c("longitude", "latitude")])
nn3 <- knn(coords, longlat = TRUE, k = 3)
z1 <- scsg2(nn3, nyw)
z2 <- flex.zones(coords, nyw, k = 3, longlat = TRUE)
all.equal(z1, z2)

jpfrench81/smerc documentation built on Jan. 13, 2024, 4:30 a.m.