% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/centrality.R
\name{hits_scores}
\alias{hits_scores}
\title{Kleinberg's hub and authority centrality scores.}
\usage{
hits_scores(
  graph,
  ...,
  scale = TRUE,
  weights = NULL,
  options = arpack_defaults()
)
}
\arguments{
\item{graph}{The input graph.}

\item{...}{These dots are for future extensions and must be empty.}

\item{scale}{Logical scalar, whether to scale the result to have a maximum
score of one. If no scaling is used then the result vector has unit length
in the Euclidean norm.}

\item{weights}{Optional positive weight vector for calculating weighted
scores. If the graph has a \code{weight} edge attribute, then this is used
by default. Pass \code{NA} to ignore the weight attribute. This function
interprets edge weights as connection strengths. The weights of parallel
edges are effectively added up.}

\item{options}{A named list, to override some ARPACK options. See
\code{\link[=arpack]{arpack()}} for details.}
}
\value{
A named list with members:
\describe{
\item{hub}{
The hub score of the vertices.
}
\item{authority}{
The authority score of the vertices.
}
\item{value}{
The corresponding eigenvalue of the calculated principal eigenvector.
}
\item{options}{
Some information about the ARPACK computation, it has the same members as the \code{options} member returned by \code{\link[=arpack]{arpack()}}, see that for documentation.
}
}
}
\description{
The hub scores of the vertices are defined as the principal eigenvector
of \eqn{A A^T}{A*t(A)}, where \eqn{A} is the adjacency matrix of the
graph.
}
\details{
Similarly, the authority scores of the vertices are defined as the principal
eigenvector of \eqn{A^T A}{t(A)*A}, where \eqn{A} is the adjacency matrix of
the graph.

For undirected matrices the adjacency matrix is symmetric and the hub
scores are the same as authority scores.
}
\section{Related documentation in the C library}{
\href{https://igraph.org/c/html/0.10.17/igraph-Structural.html#igraph_hub_and_authority_scores}{\code{hub_and_authority_scores()}}, \href{https://igraph.org/c/html/0.10.17/igraph-Basic.html#igraph_vcount}{\code{vcount()}}, \href{https://igraph.org/c/html/0.10.17/igraph-Basic.html#igraph_edges}{\code{edges()}}, \href{https://igraph.org/c/html/0.10.17/igraph-Basic.html#igraph_get_eids}{\code{get_eids()}}, \href{https://igraph.org/c/html/0.10.17/igraph-Basic.html#igraph_ecount}{\code{ecount()}}
}

\examples{
## An in-star
g <- make_star(10)
hits_scores(g)

## A ring
g2 <- make_ring(10)
hits_scores(g2)
}
\references{
J. Kleinberg. Authoritative sources in a hyperlinked
environment. \emph{Proc. 9th ACM-SIAM Symposium on Discrete Algorithms},
1998. Extended version in \emph{Journal of the ACM} 46(1999). Also appears
as IBM Research Report RJ 10076, May 1997.
}
\seealso{
\code{\link[=eigen_centrality]{eigen_centrality()}} for eigenvector centrality,
\code{\link[=page_rank]{page_rank()}} for the Page Rank scores. \code{\link[=arpack]{arpack()}} for
the underlining machinery of the computation.

Centrality measures
\code{\link{alpha_centrality}()},
\code{\link{authority_score}()},
\code{\link{betweenness}()},
\code{\link{closeness}()},
\code{\link{diversity}()},
\code{\link{eigen_centrality}()},
\code{\link{harmonic_centrality}()},
\code{\link{page_rank}()},
\code{\link{power_centrality}()},
\code{\link{spectrum}()},
\code{\link{strength}()},
\code{\link{subgraph_centrality}()}
}
\concept{centrality}
