<?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>neighbors -- returns the neighbors of a vertex or list of vertices</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_num__Connected__Components.html">next</a> | <a href="___Maximal__Edges.html">previous</a> | <a href="_num__Connected__Components.html">forward</a> | <a href="___Maximal__Edges.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>neighbors -- returns the neighbors of a vertex or list of vertices</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>N = neighbors(H,V)</tt><br/><tt>N = neighbors(H,n)</tt><br/><tt>N = neighbors(H,L)</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>
<li><span><tt>V</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a vertex</span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the index of a vertex</span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of vertices or indices of vertices</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>N</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of neighbors to the given vertex or vertices</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><div>The vertices adjacent to vertex <tt>V</tt> are called the neighbors of <tt>V</tt>. The neighbors of a list of vertices <tt>L</tt> are those vertices that are not in <tt>L</tt> and are adjacent to a vertex in <tt>L</tt>.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..f];</pre>
</td></tr>
<tr><td><pre>i2 : G = graph {a*b, a*c, a*d, d*e, d*f};</pre>
</td></tr>
<tr><td><pre>i3 : neighbors(G,a)
o3 = {b, c, d}
o3 : List</pre>
</td></tr>
<tr><td><pre>i4 : neighbors(G,0)
o4 = {b, c, d}
o4 : List</pre>
</td></tr>
<tr><td><pre>i5 : neighbors(G,{a,d})
o5 = {b, c, e, f}
o5 : List</pre>
</td></tr>
<tr><td><pre>i6 : neighbors(G,{0,3})
o6 = {b, c, e, f}
o6 : List</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_degree__Vertex.html" title="returns the degree of a vertex">degreeVertex</a> -- returns the degree of a vertex</span></li>
<li><span><a href="_vertices.html" title="gets the vertices of a (hyper)graph">vertices</a> -- gets the vertices of a (hyper)graph</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>neighbors</tt> :</h2>
<ul><li>neighbors(HyperGraph,List)</li>
<li>neighbors(HyperGraph,RingElement)</li>
<li>neighbors(HyperGraph,ZZ)</li>
</ul>
</div>
</div>
</body>
</html>
