% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/centrality.R
\name{centrality_katz}
\alias{centrality_katz}
\title{Katz Centrality}
\usage{
centrality_katz(x, katz_alpha = 0.1, ...)
}
\arguments{
\item{x}{Network input (matrix, igraph, network, cograph_network, tna object).}

\item{katz_alpha}{Attenuation factor. Must satisfy
\eqn{\alpha < 1 / \rho(A)} where \eqn{\rho(A)} is the spectral radius.
Default 0.1 matches centiserve and NetworkX conventions.}

\item{...}{Additional arguments passed to \code{\link{centrality}}.}
}
\value{
Named numeric vector of Katz centrality values.
}
\description{
Katz (1953) status index: \eqn{C = (I - \alpha A^T)^{-1} \mathbf{1}}.
Each node's score sums attenuated walks of every length back to it, with
attenuation \eqn{\alpha} applied per step. Rankings are identical to
Bonacich's alpha centrality with a uniform exogenous vector.
}
\details{
Equivalence is verified bit-exact against \code{centiserve::katzcent}
(cograph mirrors centiserve's exact LAPACK call sequence) and at machine
epsilon against \code{igraph::alpha_centrality(exo = 1)} and
\code{networkx.katz_centrality_numpy}.
}
\examples{
adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_katz(adj)
}
\references{
Katz, L. (1953). A new status index derived from sociometric analysis.
\emph{Psychometrika}, 18(1), 39-43.
}
\seealso{
\code{\link{centrality}}, \code{\link{centrality_eigenvector}},
\code{\link{centrality_pagerank}}.
}
