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<head><title>incidenceMatrix -- returns the incidence matrix of a hypergraph</title>
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<div><h1>incidenceMatrix -- returns the incidence matrix of a 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>M = incidenceMatrix 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>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, the incidence matrix of the hypergraph</span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function returns the incidence matrix of the given hypergraph <tt>H</tt>. The rows of the matrix are indexed by the variables of the hypergraph, and the columns are indexed by the edges. The (i,j)<sup>th</sup> entry in the matrix is 1 if vertex i is contained in edge j, and is 0 otherwise. The order of the rows and columns are determined by the internal order of the vertices and edges. See <a href="_edges.html" title="gets the edges of a (hyper)graph">edges</a> and <a href="_vertices.html" title="gets the vertices of a (hyper)graph">vertices</a>.</div>
<table class="examples"><tr><td><pre>i1 : S = QQ[a..f];</pre>
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<tr><td><pre>i2 : g = hyperGraph {a*b*c*d,c*e,e*f}
o2 = HyperGraph{edges => {{a, b, c, d}, {c, e}, {e, f}}}
ring => S
vertices => {a, b, c, d, e, f}
o2 : HyperGraph</pre>
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<tr><td><pre>i3 : incidenceMatrix g
o3 = | 1 0 0 |
| 1 0 0 |
| 1 1 0 |
| 1 0 0 |
| 0 1 1 |
| 0 0 1 |
6 3
o3 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i4 : T = QQ[f,e,d,c,b,a];</pre>
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<tr><td><pre>i5 : h = hyperGraph {a*b*c*d,c*e,e*f}
o5 = HyperGraph{edges => {{f, e}, {e, c}, {d, c, b, a}}}
ring => T
vertices => {f, e, d, c, b, a}
o5 : HyperGraph</pre>
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<tr><td><pre>i6 : incidenceMatrix h -- although the same graph, matrix is different since variables have different ordering
o6 = | 1 0 0 |
| 1 1 0 |
| 0 0 1 |
| 0 1 1 |
| 0 0 1 |
| 0 0 1 |
6 3
o6 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_adjacency__Matrix.html" title="returns the adjacency Matrix of a graph">adjacencyMatrix</a> -- returns the adjacency Matrix of a graph</span></li>
<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>
<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>
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<div class="waystouse"><h2>Ways to use <tt>incidenceMatrix</tt> :</h2>
<ul><li>incidenceMatrix(HyperGraph)</li>
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