View source: R/onemode_Constraint.R
computeBurtsConstraint | R Documentation |
This function computes Burt's (1992) one-mode ego constraint based upon a sociomatrix.
computeBurtsConstraint(
net,
inParallel = FALSE,
nCores = NULL,
isolates = NA,
pendants = 1
)
net |
A one-mode sociomatrix with network ties. |
inParallel |
TRUE/FALSE. TRUE indicates that parallel processing will be used to compute the statistic with the foreach package. FALSE indicates that parallel processing will not be used. Set to FALSE by default. |
nCores |
If inParallel = TRUE, the number of computing cores for parallel processing. If this value is not specified, then the function internally provides it by dividing the number of available cores in half. |
isolates |
What value should isolates be given? Set to NA by default. |
pendants |
What value should be given to pendant vertices? Set to 1 by default. |
The formula for Burt's (1992) one-mode ego constraint is:
c_{ij} = \left(p_{ij} + \sum_{q} p_{iq} p_{qj}\right)^2 \quad ; \; q \neq i \neq j
where:
p_{iq}
is formulated as: p_{iq} = \frac{z_{iq} + z_{qi}}{\sum_{j}(z_{ij} + z_{ji})} \quad ; \; i \neq j
Finally, the aggregate constraint of an ego i is:
C_{i} = \sum_{j} c_{ij}
While this function internally locates isolates (i.e., nodes who have no ties) and pendants (i.e., nodes who only have one tie), the user should specify what values for constraint are returned for them via the isolates and pendants options.
Lastly, this function allows users to compute the values in parallel via the foreach, doParallel, and parallel R packages.
The vector of ego network constraint values.
Kevin A. Carson kacarson@arizona.edu, Diego F. Leal dflc@arizona.edu
Burt, Ronald. 1992. Structural Holes: The Social Structure of Competition. Harvard University Press.
# For this example, we recreate the ego network provided in Burt (1992: 56):
BurtEgoNet <- matrix(c(
0,1,0,0,1,1,1,
1,0,0,1,0,0,1,
0,0,0,0,0,0,1,
0,1,0,0,0,0,1,
1,0,0,0,0,0,1,
1,0,0,0,0,0,1,
1,1,1,1,1,1,0),
nrow = 7, ncol = 7)
colnames(BurtEgoNet) <- rownames(BurtEgoNet) <- c("A", "B", "C", "D", "E",
"F", "ego")
#the constraint value for the ego replicates that provided in Burt (1992: 56)
computeBurtsConstraint(BurtEgoNet)
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