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<head><title>hyperGraphToSimplicialComplex -- makes a simplicial complex from a (hyper)graph</title>
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<div><h1>hyperGraphToSimplicialComplex -- makes a simplicial complex from 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>D = hyperGraphToSimplicialComplex 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>D</tt>, <span>a <a href="../../SimplicialComplexes/html/___Simplicial__Complex.html">simplicial complex</a></span>, whose facets are given by the edges of <tt>H</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function produces a simplicial complex from a (hyper)graph. The facets of the simplicial complex are given by the edge set of the (hyper)graph. This function is the inverse of <a href="_simplicial__Complex__To__Hyper__Graph.html" title="makes a (hyper)graph from a simplicial complex">simplicialComplexToHyperGraph</a> and enables users to make use of functions in the package <a href="../../SimplicialComplexes/html/index.html" title="simplicial complexes">SimplicialComplexes</a>.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x_1..x_6];</pre>
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<tr><td><pre>i2 : G = graph({x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_5,x_1*x_5,x_1*x_6,x_5*x_6}) --5-cycle and a triangle
o2 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
1 2 2 3 3 4 1 5 4 5 1 6 5 6
ring => R
vertices => {x , x , x , x , x , x }
1 2 3 4 5 6
o2 : Graph</pre>
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<tr><td><pre>i3 : DeltaG = hyperGraphToSimplicialComplex G
o3 = | x_5x_6 x_1x_6 x_4x_5 x_1x_5 x_3x_4 x_2x_3 x_1x_2 |
o3 : SimplicialComplex</pre>
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<tr><td><pre>i4 : hyperGraphDeltaG = simplicialComplexToHyperGraph DeltaG
o4 = HyperGraph{edges => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
1 2 2 3 3 4 1 5 4 5 1 6 5 6
ring => R
vertices => {x , x , x , x , x , x }
1 2 3 4 5 6
o4 : HyperGraph</pre>
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<tr><td><pre>i5 : GPrime = graph(hyperGraphDeltaG)
o5 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
1 2 2 3 3 4 1 5 4 5 1 6 5 6
ring => R
vertices => {x , x , x , x , x , x }
1 2 3 4 5 6
o5 : Graph</pre>
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<tr><td><pre>i6 : G === GPrime
o6 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_simplicial__Complex__To__Hyper__Graph.html" title="makes a (hyper)graph from a simplicial complex">simplicialComplexToHyperGraph</a> -- makes a (hyper)graph from a simplicial complex</span></li>
<li><span><a href="___Constructor_sp__Overview.html" title="a summary of the many ways of making graphs and hypergraphs">Constructor Overview</a> -- a summary of the many ways of making graphs and hypergraphs</span></li>
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<div class="waystouse"><h2>Ways to use <tt>hyperGraphToSimplicialComplex</tt> :</h2>
<ul><li>hyperGraphToSimplicialComplex(HyperGraph)</li>
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