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<head><title>adjacencyMatrix -- returns adjacency matrix of a directed graph</title>
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<div><h1>adjacencyMatrix -- returns adjacency matrix of a directed 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>M = adjacencyMatrix(G)</tt><br/><tt>M = adjacencyMatrix(P)</tt><br/><tt>M = adjacencyMatrix(I,C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>an object of class <a href="___Directed__Graph.html" title="a class for directed graphs">DirectedGraph</a></span></span></li>
<li><span><tt>P</tt>, <span>an object of class <a href="___Poset.html" title="a class for partially ordered sets (posets)">Poset</a></span></span></li>
<li><span><tt>I</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</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>, whose rows and columns are indexed by G.Vertices or P.GroundSet or I. The (i,j) entry of M is 1 if (i,j) is in G.DirectedEdges or P.Relations or C, and infinity otherwise. Diagonal entries are 0.</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : I = {a,b,c,d,e};</pre>
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<tr><td><pre>i2 : C = {(a,b),(b,c),(a,c),(a,d),(d,e)};</pre>
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<tr><td><pre>i3 : G = directedGraph(I,C);</pre>
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<tr><td><pre>i4 : P = poset(I,C);</pre>
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<tr><td><pre>i5 : adjacencyMatrix(G)
o5 = | 0 1 1 1 infinity |
| infinity 0 1 infinity infinity |
| infinity infinity 0 infinity infinity |
| infinity infinity infinity 0 1 |
| infinity infinity infinity infinity 0 |
5 5
o5 : Matrix RR <--- RR
53 53</pre>
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<tr><td><pre>i6 : adjacencyMatrix(P)
o6 = | 0 1 1 1 infinity |
| infinity 0 1 infinity infinity |
| infinity infinity 0 infinity infinity |
| infinity infinity infinity 0 1 |
| infinity infinity infinity infinity 0 |
5 5
o6 : Matrix RR <--- RR
53 53</pre>
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<tr><td><pre>i7 : adjacencyMatrix(I,C)
o7 = | 0 1 1 1 infinity |
| infinity 0 1 infinity infinity |
| infinity infinity 0 infinity infinity |
| infinity infinity infinity 0 1 |
| infinity infinity infinity infinity 0 |
5 5
o7 : Matrix RR <--- RR
53 53</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>Diagonal entries are 0. Output matrix is over RR.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Directed__Graph.html" title="a class for directed graphs">DirectedGraph</a> -- a class for directed graphs</span></li>
<li><span><a href="_all__Pairs__Shortest__Path.html" title="computes lengths of shortest paths between all pairs in a directed graph">allPairsShortestPath</a> -- computes lengths of shortest paths between all pairs in a directed graph</span></li>
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<div class="waystouse"><h2>Ways to use <tt>adjacencyMatrix</tt> :</h2>
<ul><li>adjacencyMatrix(DirectedGraph)</li>
<li>adjacencyMatrix(List,List)</li>
<li>adjacencyMatrix(Poset)</li>
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