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<head><title>lineGraph -- returns the line graph of a (hyper)graph</title>
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<div><h1>lineGraph -- returns the line graph of a (hyper)graph</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 = lineGraph H</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="___Graph.html">graph</a></span>, the line graph of <tt>H</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><div>The line graph <tt>L</tt> of a hypergraph <tt>H</tt> has a vertex for each edge in <tt>H</tt>. Two vertices in <tt>L</tt> are adjacent if their edges in <tt>H</tt> share a vertex. The order of the vertices in <tt>L</tt> are determined by the implict order on the edges of <tt>H</tt>. See <a href="_edges.html" title="gets the edges of a (hyper)graph">edges</a>.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..e];</pre>
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<tr><td><pre>i2 : G = graph {a*b,a*c,a*d,d*e}
o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {d, e}}}
ring => R
vertices => {a, b, c, d, e}
o2 : Graph</pre>
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<tr><td><pre>i3 : lineGraph G
o3 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }}}
0 1 0 2 1 2 2 3
ring => QQ[x , x , x , x ]
0 1 2 3
vertices => {x , x , x , x }
0 1 2 3
o3 : Graph</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_edges.html" title="gets the edges of a (hyper)graph">edges</a> -- gets the edges of a (hyper)graph</span></li>
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<div class="waystouse"><h2>Ways to use <tt>lineGraph</tt> :</h2>
<ul><li>lineGraph(HyperGraph)</li>
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