sedist {blockmodeling}

Computes distances in terms of Structural equivalence (Lorrain & White, 1971)

Description

The functions compute the distances in terms of Structural equivalence (Lorrain and White, 1971) between the units of a one-mode network. Several options for treating the diagonal values are supported.

Usage

sedist(
  M,
  method = "default",
  fun = "default",
  fun.on.rows = "default",
  handle.interaction = "switch",
  use = "pairwise.complete.obs",
  ...
)

Arguments

M

A matrix representing the (usually valued) network. For now, only one-relational networks are supported. The network must be one-mode.

method

The method used to compute distances - any of the methods allowed by functions dist, "cor" or "cov" (all package::stats) or just "cor" or "cov" (given as a character).

fun

Which function should be used to compute distances (given as a character).

fun.on.rows

For non-standard function - does the function compute measure on rows (such as "cor", "cov",...) of the data matrix (as opposed to computing measure on columns (such as dist).

handle.interaction

How should the interaction between the vertices analysed be handled:
"switch" (the default) - assumes that when comparing units i and j, M[i,i] should be compared with M[j,j] and M[i,j] with M[j,i]. These two comparisons are weighted by 2. This should be used with Euclidean distance to get the corrected Euclidean distance with p = 2.
"switch2" - the same (alias)
"switch1" - the same as above, only that the two comparisons are weighted by 1. This should be used with Euclidean distance to get the corrected Wuclidean distance with p = 1.
"ignore" (diagonal) - Diagonal is ignored. This should be used with Euclidean distance to get the corrected Euclidean distance with p = 0.
"none" - the matrix is used "as is"

use

For use with methods "cor" and "cov", for other methods (the default option should be used if handle.interaction == "ignore"), "pairwise.complete.obs" are always used, if stats.dist.cor.cov = TRUE.

...

Additional arguments to fun

Details

If both method and fun are "default", the Euclidean distances are computed. The "default" method for fun = "dist" is "euclidean" and for fun = "cor" "pearson".

Value

A matrix (usually of class dist) is returned.

Author(s)

Aleš Žiberna

References

Batagelj, V., Ferligoj, A., & Doreian, P. (1992). Direct and indirect methods for structural equivalence. Social Networks, 14(1-2), 63-90. doi: 10.1016/0378-8733(92)90014-X

Lorrain, F., & White, H. C. (1971). Structural equivalence of individuals in social networks. Journal of Mathematical Sociology, 1(1), 49-80. doi: 10.1080/0022250X.1971.9989788

See Also

dist, hclust, REGE, optParC, optParC, optRandomParC

Examples

# Generating a simple network corresponding to the simple Sum of squares
# Structural equivalence with blockmodel:
# null com
# null null
n <- 20
net <- matrix(NA, ncol = n, nrow = n)
clu <- rep(1:2, times = c(5, 15))
tclu <- table(clu)
net[clu == 1, clu == 1] <- rnorm(n = tclu[1] * tclu[1], mean = 0, sd = 1)
net[clu == 1, clu == 2] <- rnorm(n = tclu[1] * tclu[2], mean = 4, sd = 1)
net[clu == 2, clu == 1] <- rnorm(n = tclu[2] * tclu[1], mean = 0, sd = 1)
net[clu == 2, clu == 2] <- rnorm(n = tclu[2] * tclu[2], mean = 0, sd = 1)

D <- sedist(M = net)
plot.mat(net, clu = cutree(hclust(d = D, method = "ward"), k = 2))