<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>isolatedVertices -- returns all vertices not contained in any edge</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_is__Perfect.html">next</a> | <a href="_is__Leaf.html">previous</a> | <a href="_is__Perfect.html">forward</a> | <a href="_is__Leaf.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>isolatedVertices -- returns all vertices not contained in any edge</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>L = isolatedVertices(H)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, all vertices that are not contained in any edge of <tt>H</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><div>A vertex of a hypergraph is called isolated if it is not contained in any edges. Vertices in a hypergraph that are contained in an edge of size one are not considered to be isolated.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a,b,c,d,e];</pre>
</td></tr>
<tr><td><pre>i2 : G = graph {a*b,c*d}
o2 = Graph{edges => {{a, b}, {c, d}} }
ring => R
vertices => {a, b, c, d, e}
o2 : Graph</pre>
</td></tr>
<tr><td><pre>i3 : isolatedVertices G
o3 = {e}
o3 : List</pre>
</td></tr>
<tr><td><pre>i4 : H = hyperGraph {a*b,c}
o4 = HyperGraph{edges => {{a, b}, {c}} }
ring => R
vertices => {a, b, c, d, e}
o4 : HyperGraph</pre>
</td></tr>
<tr><td><pre>i5 : isolatedVertices H
o5 = {d, e}
o5 : List</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_connected__Components.html" title="returns the connected components of a hypergraph">connectedComponents</a> -- returns the connected components of a hypergraph</span></li>
<li><span><a href="_is__Connected.html" title="determines if a (hyper)graph is connected">isConnected</a> -- determines if a (hyper)graph is connected</span></li>
<li><span><a href="_num__Connected__Components.html" title="returns the number of connected components in a (hyper)graph">numConnectedComponents</a> -- returns the number of connected components in a (hyper)graph</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>isolatedVertices</tt> :</h2>
<ul><li>isolatedVertices(HyperGraph)</li>
</ul>
</div>
</div>
</body>
</html>
