sedist function

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

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. UTF-8

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

Returns

A matrix (usually of class dist) is returned.

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".

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))

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

Author(s)