computeLealBrokerage: Compute Potential for Cultural Brokerage (PIB) Based on Leal...

In dream: Dynamic Relational Event Analysis and Modeling

Compute Potential for Cultural Brokerage (PIB) Based on Leal (2025)

Description

Following Leal (2025), this function calculates node’s Potential for Intercultural Brokerage (PIB) in a one-mode network. For example, users can examine PIB across gender. The option count determines what is returned by the function. If count is true, then the count of culturally dissimilar pairs brokered by ego is included (i.e., ego’s total count of brokered open triangles where the alters at the two endpoints of said open triangles are culturally dissimilar from one another). If count is false, the proportion of ego’s brokered open triangles where the endpoints are culturally dissimilar out of all of ego’s brokered open triangles (regardless of the cultural identity of the alters) is returned. The formula for computing interpersonal brokerage is presented in the details section.

Usage

computeLealBrokerage(
  net,
  g.mem,
  symmetric = TRUE,
  triad.type = NULL,
  count = TRUE,
  isolate = NA
)

Arguments

net	The one-mode adjacency matrix.
g.mem	The vector of membership values that the brokerage scores will be based on.
symmetric	TRUE/FALSE. TRUE indicates that network matrix will be treated as symmetric. FALSE indicates that the network matrix will be treated as asymmetric. Set to TRUE by default.
triad.type	The string value (or vector) that indicates what specific triadic (star) structures the potential for cultural brokerage will be computed for. Possible values are "ANY", "OTS", "ITS", "MTS" (see the details section). The function defaults to “ANY”.
count	TRUE/FALSE. TRUE indicates that the number of culturally brokered open triangles will be returned. FALSE indicates that the proportion of culturally brokered open triangles to all open triangles will be returned (see the details section). Set to TRUE by default.
isolate	If count = FALSE, the numerical value that will be given to isolates. This value is set to NA by default, as 0/0 is undefined. The user can specify this value!

Details

Following Leal (2025), the formula for interpersonal brokerage is:

\text{PIB}_i = \sum_{j < k} \frac{S_{jik}}{S_{jk}} m_{jk}, \quad S_{jik} \neq 0 \text{ and } i \neq j \neq k

where:

• S_{jik} = 1 if there is an (un)directed two-path connecting actors j and k through actor i; 0 otherwise.

• m_{jk} = 1 if actors j and k are on different sides of a symbolic boundary; 0 otherwise.

• Following Gould (1989), S_{jik} represents the total number of two-paths between actors j and k.

If the network is non-symmetric (i.e., the user specified symmetric = FALSE), then the function can compute the cultural brokerage scores for different star structures. The possible values are: "ANY", which computes the scores for all structures, where a tie exists between i and j, j and k, and one does not exist between i and k. "OTS" computes the values for outgoing two-stars (i<-j->k or the 021D triad according to the M.A.N. notation; see Wasserman and Faust 1994), where j is the broker. "ITS" computes the values for incoming two-stars (i->j<-k or the 021U triad according to the M.A.N. notation; see Wasserman and Faust 1994 ), where j is the broker. "MTS" computes PIB for mixed triadic structures (i<-j<-k or i->j->k or the 021C triad according to the M.A.N. notation; see Wasserman and Faust 1994). If not specified, the function defaults to the "ANY" category. This function can also compute all of the formations at once.

Value

The vector of interpersonal cultural brokerage values for the one-mode network.

Author(s)

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

References

Gould, Roger. 1989. "Power and Social Structure in Community Elites." Social Forces 68(2): 531-552.

Leal, Diego F. 2025. "Locating Cultural Holes Brokers in Diffusion Dynamics Across Bright Symbolic Boundaries." Sociological Methods & Research \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/00491241251322517")}

Wasserman, Stanley and Katherine Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

Examples

# For this example, we recreate Figure 3 in Leal (2025)
LealNet <- matrix( c(
 0,1,0,0,0,0,0,
 1,0,1,1,0,0,0,
 0,1,0,0,1,1,0,
 0,1,0,0,1,0,0,
 0,0,1,1,0,0,0,
 0,0,1,0,0,0,1,
 0,0,0,0,0,1,0),
 nrow = 7, ncol = 7, byrow = TRUE)

colnames(LealNet) <- rownames(LealNet) <- c("A", "B", "C","D",
                                           "E", "F", "G")
categorical_variable <- c(0,0,1,0,0,0,0)
#These values are exactly the same as reported by Leal (2025)
computeLealBrokerage(LealNet,
   symmetric = TRUE,
   g.mem = categorical_variable)

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