# is.separator

0th

Percentile

##### Vertex separators

These functions check whether a given set of vertices is a vertex separator, or a minimal vertex separator.

Keywords
graphs
##### Usage
is.separator(graph, candidate)
is.minimal.separator(graph, candidate)
##### Arguments
graph
The input graph. It may be directed, but edge directions are ignored.
candidate
A numeric vector giving the vertex ids of the candidate separator.
##### Details

is.separator decides whether the supplied vertex set is a vertex separator. A vertex set is a vertex separator if its removal results a disconnected graph.

is.minimal.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 subsets is a vertex separator.

In the special case of a fully connected graph with $n$ vertices, each set of $n-1$ vertices is considered to be a vertex separator.

##### Value

• A logical scalar, whether the supplied vertex set is a (minimal) vertex separator or not.

##### concept

Vertex separator

minimum.size.separators lists all vertex separator of minimum size.

##### Aliases
• is.separator
• is.minimal.separator
##### Examples
# The graph from the Moody-White paper
mw <- graph.formula(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 <- minimum.size.separators(G)
sapply(sep, is.minimal.separator, graph=G)
}

check.sep(mw)
check.sep(mw1)
check.sep(mw2)
check.sep(mw3)
check.sep(mw4)
check.sep(mw5)
Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)

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