brokerage.j: Positional analysis of j and k in the Brokerage relationship...

In huhn1234/vogeltools: Utilities for the social network analysis

Description

brokerage.j and brokerage.k counts the number of times the alter stands at the position in j and k, respectively, in the different brokerage typology

Usage

brokerage.j(
  mat = mat,
  attr = attr,
  method = "abs.diff",
  alpha = 0.5,
  denom = "none"
)

brokerage.k(
  mat = mat,
  attr = attr,
  method = "abs.diff",
  alpha = 0.5,
  denom = "none"
)

Arguments

mat	a matrix of a graph.
attr	a vector of attributes.
method	"abs.diff" or "match". This is a intiger indicating the method how to calculate the difference of the attr between i and j. The default method "abs.diff" take the absolute abs(attr[i]-attr[j]). "match" code 1 if attr[i]==attr[j] and 0 otherwise.
alpha	a cut-off value to differentiate homophilous and heterophilious ties. If the difference of attr values between i and j exceeds the value of alpha, then the relationship between i and j is treated as heterophilious relationship. Otherwise homophilous.
denom	"none"(default), "n" or "density". A integer indicating how to standardize the counted number of times an actor stands at the j position.

Details

This function first differentiate the ties into homophilous and heterophilious ties. It counts then how many times the alter stands in the j position in the i-j-k relationship from the perspective of i. In the result matrix the value of the cell M[i,j] indicates the number of times the alter j stands in the j position. The count is standardized in accordance to the method defined in denom. Brokerage analysis was first introduced in Gould and Fernandez (1989). This function modifies the original concept in a way that we construct the brokerage typology not based on the subgroup that consists of actors engaging in the same issues, but the homophily and heterophily ties.

In the brokerage relationship where i and j as well as j and k are connected AND i and k is not connected,

Coordinator (wi) is the relationship where i->j and j->k is homophilous ties;

Itinerant broker (wo) is the one where i->j and j->k is heterophilious ties;

Representative (bio) is the one where i->j is a homophilous and j->k is a heterophilious tie;

Gatekeeper (boi) is the one where i->j is a heterophilious and j->k is a homophilous tie.

The fifth type, liaison, in the original literature (Gould and Fernandez 1989) does not come up in this function due to the aforementioned modification: the heterophiles tie between i->j and j->k already implies the same type to itinerant broker(bo).

The returned matrix M[i,j] is standardized if it is selected in "denom". "n" returns the value M[i,j]/n where n is number of actors in the mat. "density" returns M[i,j]*density(mat).

Value

a list of matrices in which each matrix shows the result of each typology.

References

Gould, Roger V. and Roberto M. Fernandez. (1989). "Structures of Mediation: A Formal Approach to Brokerage in Transaction Networks," Sociological Methodology 19: 89-126.

Examples

library(sna)
mat <- sna::rgraph(5, tprob = 0.5, mode = "graph")
dimnames(mat) <- list(LETTERS[1:5],LETTERS[1:5])
attr <- c(1,1,1,0,0)
gplot(mat, displaylabels = TRUE, vertex.col = attr, usearrows = FALSE)

brokerage.j(mat, attr, "match")
brokerage.j(mat, attr, "match", denom = "n")

huhn1234/vogeltools documentation built on Jan. 17, 2020, 5:21 p.m.