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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Minimal vertex separators</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for is_min_separator {igraph}"><tr><td>is_min_separator {igraph}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Minimal vertex separators</h2> <h3>Description</h3> <p>Check whether a given set of vertices is a minimal vertex separator. </p> <h3>Usage</h3> <pre> is_min_separator(graph, candidate) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>graph</code></td> <td> <p>The input graph. It may be directed, but edge directions are ignored.</p> </td></tr> <tr valign="top"><td><code>candidate</code></td> <td> <p>A numeric vector giving the vertex ids of the candidate separator.</p> </td></tr> </table> <h3>Details</h3> <p><code>is_min_separator</code> 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. </p> <p>In the special case of a fully connected graph with <i>n</i> vertices, each set of <i>n-1</i> vertices is considered to be a vertex separator. </p> <h3>Value</h3> <p>A logical scalar, whether the supplied vertex set is a (minimal) vertex separator or not. </p> <h3>See Also</h3> <p><code><a href="min_separators.html">min_separators</a></code> lists all vertex separator of minimum size. </p> <h3>Examples</h3> <pre> # 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) </pre> <hr /><div style="text-align: center;">[Package <em>igraph</em> version 1.3.5 <a href="00Index.html">Index</a>]</div> </body></html>