% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/centrality.R
\name{centrality_brokerage_representative}
\alias{centrality_brokerage_representative}
\title{Gould-Fernandez Brokerage — Representative Role}
\usage{
centrality_brokerage_representative(x, membership = NULL, ...)
}
\arguments{
\item{x}{Directed network input (matrix, igraph, cograph_network, tna object).}

\item{membership}{Integer or character vector of group assignments, length
equal to the number of nodes. Required.}

\item{...}{Additional arguments passed to \code{\link{centrality}}.}
}
\value{
Named integer vector of representative role counts.
}
\description{
Representative brokerage (b_IO): count of open directed 2-paths
\eqn{A \to V \to B} where \eqn{A} and \eqn{V} are in the same group
and \eqn{B} is in a different group. The broker represents their group
outward.
}
\details{
Bit-exact match against \code{sna::brokerage$raw.nli[, "b_IO"]}.
Directed-only.
}
\examples{
adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_representative(adj, membership = c(1, 1, 2, 2))
}
\references{
Gould & Fernandez (1989).
}
\seealso{
\code{\link{centrality_brokerage_coordinator}}.
}
