% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/centrality.R
\name{centrality_reaching_local}
\alias{centrality_reaching_local}
\title{Local Reaching Centrality (Mones, Vicsek & Vicsek 2012)}
\usage{
centrality_reaching_local(x, mode = "all", ...)
}
\arguments{
\item{x}{Network input (matrix, igraph, network, cograph_network, tna object).}

\item{mode}{For directed networks: \code{"all"} (default), \code{"in"}, or
\code{"out"}.}

\item{...}{Additional arguments passed to \code{\link{centrality}}.}
}
\value{
Named numeric vector of local reaching centrality values.
}
\description{
Local reaching centrality measures how much of the network is reachable
from a node.
}
\details{
\itemize{
\item Directed unweighted: \eqn{LRC(v) = |\{u : u \ne v, v \to u\}| / (N - 1)}.
\item Undirected unweighted: average of \eqn{1/d(v, u)} over all
\eqn{u \ne v}, divided by \eqn{N - 1}. Numerically equal to
\code{igraph::harmonic_centrality(normalized = TRUE)}.
\item Weighted: NetworkX convention, where edge weights are interpreted
as strengths and path length is \eqn{\sum_e (\mathrm{total\_weight} / w_e)}.
Per-path score is the mean of original edge weights along the shortest
path.
}

Bit-exact match against \code{networkx.local_reaching_centrality} across
all three branches. Bit-exact match against
\code{igraph::harmonic_centrality(normalized = TRUE)} for the undirected
unweighted branch. See \code{\link{reaching_global}} for the graph-level
hierarchy measure derived from per-node LRC.
}
\examples{
# Directed path A -> B -> C
adj <- matrix(c(0,1,0, 0,0,1, 0,0,0), 3, 3, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_reaching_local(adj, mode = "out")
}
\references{
Mones, E., Vicsek, L., & Vicsek, T. (2012). Hierarchy measure for complex
networks. \emph{PLoS ONE}, 7(3), e33799.
}
\seealso{
\code{\link{centrality}}, \code{\link{centrality_harmonic}},
\code{\link{reaching_global}}.
}
