% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/flow.R
\name{is_min_separator}
\alias{is_min_separator}
\title{Minimal vertex separators}
\usage{
is_min_separator(graph, candidate)
}
\arguments{
\item{graph}{The input graph. It may be directed, but edge directions are
ignored.}

\item{candidate}{A numeric vector giving the vertex ids of the candidate
separator.}
}
\value{
A logical scalar, whether the supplied vertex set is a (minimal)
vertex separator or not.
}
\description{
Check whether a given set of vertices is a minimal vertex separator.
}
\details{
\code{is_min_separator()} decides whether the supplied vertex set is a minimal
vertex separator. A minimal vertex separator is a vertex separator, such
that none of its proper subsets are a vertex separator.
}
\section{Related documentation in the C library}{
\href{https://igraph.org/c/html/0.10.17/igraph-Separators.html#igraph_is_minimal_separator}{\code{is_minimal_separator()}}, \href{https://igraph.org/c/html/0.10.17/igraph-Basic.html#igraph_vcount}{\code{vcount()}}
}

\examples{
# The graph from the Moody-White paper
mw <- graph_from_literal(
  1 - 2:3:4:5:6, 2 - 3:4:5:7, 3 - 4:6:7, 4 - 5:6:7,
  5 - 6:7:21, 6 - 7, 7 - 8:11:14:19, 8 - 9:11:14, 9 - 10,
  10 - 12:13, 11 - 12:14, 12 - 16, 13 - 16, 14 - 15, 15 - 16,
  17 - 18:19:20, 18 - 20:21, 19 - 20:22:23, 20 - 21,
  21 - 22:23, 22 - 23
)

# Cohesive subgraphs
mw1 <- induced_subgraph(mw, as.character(c(1:7, 17:23)))
mw2 <- induced_subgraph(mw, as.character(7:16))
mw3 <- induced_subgraph(mw, as.character(17:23))
mw4 <- induced_subgraph(mw, as.character(c(7, 8, 11, 14)))
mw5 <- induced_subgraph(mw, as.character(1:7))

check.sep <- function(G) {
  sep <- min_separators(G)
  sapply(sep, is_min_separator, graph = G)
}

check.sep(mw)
check.sep(mw1)
check.sep(mw2)
check.sep(mw3)
check.sep(mw4)
check.sep(mw5)

}
\seealso{
Other flow: 
\code{\link{dominator_tree}()},
\code{\link{edge_connectivity}()},
\code{\link{is_separator}()},
\code{\link{max_flow}()},
\code{\link{min_cut}()},
\code{\link{min_separators}()},
\code{\link{min_st_separators}()},
\code{\link{st_cuts}()},
\code{\link{st_min_cuts}()},
\code{\link{vertex_connectivity}()}
}
\concept{flow}
