computeBurtsES: Compute Burt's (1992) Effective Size for Ego Networks from a...

In dream: Dynamic Relational Event Analysis and Modeling

Compute Burt's (1992) Effective Size for Ego Networks from a Sociomatrix

Description

This function computes Burt's (1992) one-mode ego effective size based upon a sociomatrix (see details).

Usage

computeBurtsES(
  net,
  inParallel = FALSE,
  nCores = NULL,
  isolates = NA,
  pendants = 1
)

Arguments

net	The 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	The numerical value that represents what value will isolates be given. Set to NA by default.
pendants	The numerical value that represents what value will pendant vertices be given. Set to 1 by default.

Details

The formula for Burt's (1992; see also Borgatti 1997) one-mode ego effective size is:

E_{i} = \sum_{j} 1 - \sum_{q}p_{iq}m_{jq} ; q \neq i \neq j

where E_{i} is the ego effective size for an ego i. p_{iq} is formulated as:

\frac{(z_{iq} + z_{qi}) }{\sum_{j}(z_{ij} + z_{ji})} ; i \neq j

and m_{jq} is:

m_{jq} = \frac{(z_{jq} + z_{qj})}{max(z_{jk} + z_{kj})}

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.

Value

The vector of ego network effective size values.

Author(s)

Kevin A. Carson [e-mail], Diego F. Leal [e-mail]

References

Burt, Ronald. 1992. Structural Holes: The Social Structure of Competition. Harvard University Press.

Borgatti, Stephen. 1997. "Structural Holes: Unpacking Burt's Redundancy Measures." Connections 20(1): 35-38.

Examples

# For this example, we recreate the ego network provided in Borgatti (1997):
BorgattiEgoNet <- matrix(
 c(0,1,0,0,0,0,0,0,1,
   1,0,0,0,0,0,0,0,1,
   0,0,0,1,0,0,0,0,1,
   0,0,1,0,0,0,0,0,1,
   0,0,0,0,0,1,0,0,1,
  0,0,0,0,1,0,0,0,1,
  0,0,0,0,0,0,0,1,1,
   0,0,0,0,0,0,1,0,1,
   1,1,1,1,1,1,1,1,0),
 nrow = 9, ncol = 9, byrow = TRUE)
colnames(BorgattiEgoNet) <- rownames(BorgattiEgoNet) <- c("A", "B", "C",
                                                         "D", "E", "F",
                                                        "G", "H", "ego")
#the effective size value for the ego replicates that provided in Borgatti (1997)
computeBurtsES(BorgattiEgoNet)

# 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 effective size value for the ego replicates that provided in Burt (1992: 56)
computeBurtsES(BurtEgoNet)

dream documentation built on Aug. 8, 2025, 6:36 p.m.