% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/centralization.R
\name{centr_eigen}
\alias{centr_eigen}
\title{Centralize a graph according to the eigenvector centrality of vertices}
\usage{
centr_eigen(
  graph,
  directed = FALSE,
  scale = deprecated(),
  options = arpack_defaults(),
  normalized = TRUE
)
}
\arguments{
\item{graph}{The input graph.}

\item{directed}{logical scalar, whether to use directed shortest paths for
calculating eigenvector centrality.}

\item{scale}{\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}} Ignored. Computing
eigenvector centralization requires normalized eigenvector centrality scores.}

\item{options}{This is passed to \code{\link[=eigen_centrality]{eigen_centrality()}}, the options
for the ARPACK eigensolver.}

\item{normalized}{Logical scalar. Whether to normalize the graph level
centrality score by dividing by the theoretical maximum.}
}
\value{
A named list with the following components:
\describe{
\item{vector}{
The node-level centrality scores.
}
\item{value}{
The corresponding eigenvalue.
}
\item{options}{
ARPACK options, see the return value of \code{\link[=eigen_centrality]{eigen_centrality()}} for details.
}
\item{centralization}{
The graph level centrality index.
}
\item{theoretical_max}{
The same as above, the theoretical maximum centralization score
for a graph with the same number of vertices.
}
}
}
\description{
See \code{\link[=centralize]{centralize()}} for a summary of graph centralization.
}
\section{Related documentation in the C library}{
\href{https://igraph.org/c/html/0.10.17/igraph-Structural.html#igraph_centralization_eigenvector_centrality}{\code{centralization_eigenvector_centrality()}}
}

\examples{
# A BA graph is quite centralized
g <- sample_pa(1000, m = 4)
centr_degree(g)$centralization
centr_clo(g, mode = "all")$centralization
centr_betw(g, directed = FALSE)$centralization
centr_eigen(g, directed = FALSE)$centralization

# The most centralized graph according to eigenvector centrality
g0 <- make_graph(c(2, 1), n = 10, dir = FALSE)
g1 <- make_star(10, mode = "undirected")
centr_eigen(g0)$centralization
centr_eigen(g1)$centralization
}
\seealso{
Other centralization related: 
\code{\link{centr_betw}()},
\code{\link{centr_betw_tmax}()},
\code{\link{centr_clo}()},
\code{\link{centr_clo_tmax}()},
\code{\link{centr_degree}()},
\code{\link{centr_degree_tmax}()},
\code{\link{centr_eigen_tmax}()},
\code{\link{centralize}()}
}
\concept{centralization related}
