% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/decomposition.R
\name{is_chordal}
\alias{is_chordal}
\alias{is.chordal}
\title{Chordality of a graph}
\usage{
is_chordal(
  graph,
  alpha = NULL,
  alpham1 = NULL,
  fillin = FALSE,
  newgraph = FALSE
)
}
\arguments{
\item{graph}{The input graph. It may be directed, but edge directions are
ignored, as the algorithm is defined for undirected graphs.}

\item{alpha}{Numeric vector, the maximal chardinality ordering of the
vertices. If it is \code{NULL}, then it is automatically calculated by
calling \code{\link{max_cardinality}}, or from \code{alpham1} if
that is given..}

\item{alpham1}{Numeric vector, the inverse of \code{alpha}. If it is
\code{NULL}, then it is automatically calculated by calling
\code{\link{max_cardinality}}, or from \code{alpha}.}

\item{fillin}{Logical scalar, whether to calculate the fill-in edges.}

\item{newgraph}{Logical scalar, whether to calculate the triangulated graph.}
}
\value{
A list with three members: \item{chordal}{Logical scalar, it is
\code{TRUE} iff the input graph is chordal.} \item{fillin}{If requested,
then a numeric vector giving the fill-in edges. \code{NULL} otherwise.}
\item{newgraph}{If requested, then the triangulated graph, an \code{igraph}
object. \code{NULL} otherwise.}
}
\description{
A graph is chordal (or triangulated) if each of its cycles of four or more
nodes has a chord, which is an edge joining two nodes that are not adjacent
in the cycle. An equivalent definition is that any chordless cycles have at
most three nodes.
}
\details{
The chordality of the graph is decided by first performing maximum
cardinality search on it (if the \code{alpha} and \code{alpham1} arguments
are \code{NULL}), and then calculating the set of fill-in edges.

The set of fill-in edges is empty if and only if the graph is chordal.

It is also true that adding the fill-in edges to the graph makes it chordal.
}
\examples{

## The examples from the Tarjan-Yannakakis paper
g1 <- graph_from_literal(A-B:C:I, B-A:C:D, C-A:B:E:H, D-B:E:F,
                E-C:D:F:H, F-D:E:G, G-F:H, H-C:E:G:I,
                I-A:H)
max_cardinality(g1)
is_chordal(g1, fillin=TRUE)

g2 <- graph_from_literal(A-B:E, B-A:E:F:D, C-E:D:G, D-B:F:E:C:G,
                E-A:B:C:D:F, F-B:D:E, G-C:D:H:I, H-G:I:J,
                I-G:H:J, J-H:I)
max_cardinality(g2)
is_chordal(g2, fillin=TRUE)

}
\references{
Robert E Tarjan and Mihalis Yannakakis. (1984). Simple
linear-time algorithms to test chordality of graphs, test acyclicity of
hypergraphs, and selectively reduce acyclic hypergraphs.  \emph{SIAM Journal
of Computation} 13, 566--579.
}
\seealso{
\code{\link{max_cardinality}}
}
\author{
Gabor Csardi \email{csardi.gabor@gmail.com}
}
\keyword{graphs}
