computeBCConstraint: Compute Burchard and Cornwell's (2018) Two-Mode Constraint
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computeBCConstraint

R Documentation

Compute Burchard and Cornwell's (2018) Two-Mode Constraint

Description

This function calculates the values for two-mode network constraint for weighted and unweighted two-mode networks based on Burchard and Cornwell (2018).

Usage

computeBCConstraint(net, isolates = NA, returnCIJmat = FALSE, weighted = FALSE)

Arguments

`net`	A two-mode adjacency matrix or affiliation matrix.
`isolates`	What value should isolates be given? Preset to be NA.
`returnCIJmat`	TRUE/FALSE. TRUE indicates that the full constraint matrix, that is, the network constraint from an alter j on node i, will be returned to the user. FALSE indicates that the total constraint will be returned. Set to FALSE by default.
`weighted`	TRUE/FALSE. TRUE indicates the statistic will be based on the weighted formula (see the details section). FALSE indicates the statistic will be based on the original non-weighted formula. Set to FALSE by default.

Details

Following Burchard and Cornwell (2018), the formula for two-mode constraint is:

c_{ij} = \left(\frac{|\zeta(j) \cap \zeta(i)|}{|\zeta^{(i*)}|}\right)^2

where:

c_{ij} is the constraint of ego i with respect to actor j.
|\zeta(j) \cap \zeta(i)| is the number of opposite-class contacts that i and j both share.
The denominator, |\zeta^{(i*)}|, represents the total number of opposite-class contacts of ego i excluding pendants (level 2 groups that only have one member).

The total constraint for ego i is given by:

C_{i} = \sum_{j \in \sigma(i)} c_{ij}

The function returns the aggregate constraint for each actor; however, the user can specify the function to return the constraint matrix by setting returnCIJmat to TRUE.

The function can also compute constraint for weighted two-mode networks by setting weighted to TRUE. The formula for two-mode weighted constraint is:

c_{ij} = \left(\frac{|\zeta(j) \cap \zeta(i)|}{|\zeta^{(i*)}|}\right)^2 \times w_{t}

where w_{t} is the average of the tie weights that i and j send to their shared opposite-class contacts.

Value

The vector of two-mode constraint scores for level 1 actors in a two-mode network.

Author(s)

Kevin A. Carson kacarson@arizona.edu, Diego F. Leal dflc@arizona.edu

References

Burchard, Jake and Benjamin Cornwell. 2018. "Structural Holes and Bridging in Two-Mode Networks." Social Networks 55:11-20.

Examples


# For this example, we recreate Figure 2 in Burchard and Cornwell (2018: 13)
BCNet <- matrix(
 c(1,1,0,0,
   1,0,1,0,
   1,0,0,1,
   0,1,1,1),
 nrow = 4, ncol = 4, byrow = TRUE)
colnames(BCNet) <- c("1", "2", "3", "4")
rownames(BCNet) <- c("i", "j", "k", "m")
#library(sna) #To plot the two mode network, we use the sna R package
#gplot(BCNet, usearrows = FALSE,
#      gmode = "twomode", displaylabels = TRUE)
computeBCConstraint(BCNet)

#For this example, we recreate Figure 9 in Burchard and Cornwell (2018:18) for
#weighted two mode networks.
BCweighted <- matrix(c(1,2,1, 1,0,0,
                      0,2,1,0,0,1),
                    nrow = 4, ncol = 3,
                    byrow = TRUE)
rownames(BCweighted) <- c("i", "j", "k", "l")
computeBCConstraint(BCweighted, weighted = TRUE)

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