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<head><title>complementGraph -- returns the complement of a graph or hypergraph</title>
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<div><h1>complementGraph -- returns the complement of a graph or hypergraph</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>g = complementGraph G</tt><br/><tt>h = complementGraph H</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>a <a href="___Graph.html">graph</a></span></span></li>
<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>g</tt>, <span>a <a href="___Graph.html">graph</a></span>, the complement of G, whose edges are the set of edges not in G</span></li>
<li><span><tt>h</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span>, the complement of H, whose edge set is found by taking the complement of each edge of H in the vertex set</span></li>
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<div class="single"><h2>Description</h2>
<div><div>The function <tt>complementGraph</tt> finds the complement of a graph and hypergraph. Note that this function behaves differently depending upon the type of input. When applied to a graph, complementGraph returns the graph whose edge set is the set of edges not in G. When applied to a hypergraph, the edge set is found by taking the complement of each edge of H in the vertex set.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a,b,c,d,e];</pre>
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<tr><td><pre>i2 : c5 = graph {a*b,b*c,c*d,d*e,e*a}; -- graph of the 5-cycle</pre>
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<tr><td><pre>i3 : complementGraph c5 -- the graph complement of the 5-cycle
o3 = Graph{edges => {{b, d}, {a, d}, {c, e}, {b, e}, {a, c}}}
ring => R
vertices => {a, b, c, d, e}
o3 : Graph</pre>
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<tr><td><pre>i4 : c5hypergraph = hyperGraph c5 -- the 5-cycle, but viewed as a hypergraph
o4 = HyperGraph{edges => {{a, b}, {b, c}, {c, d}, {a, e}, {d, e}}}
ring => R
vertices => {a, b, c, d, e}
o4 : HyperGraph</pre>
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<tr><td><pre>i5 : complementGraph c5hypergraph
o5 = HyperGraph{edges => {{c, d, e}, {a, d, e}, {b, a, e}, {c, b, d}, {c, b, a}}}
ring => R
vertices => {a, b, c, d, e}
o5 : HyperGraph</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>Notice that <tt>complementGraph</tt> works differently on graphs versus hypergraphs.</div>
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<div class="waystouse"><h2>Ways to use <tt>complementGraph</tt> :</h2>
<ul><li>complementGraph(Graph)</li>
<li>complementGraph(HyperGraph)</li>
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