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<head><title>adjacencyMatrix -- returns the adjacency Matrix of a graph</title>
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<div><h1>adjacencyMatrix -- returns the adjacency Matrix of a 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></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>
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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 adjacency matrix of the graph</span></li>
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<div class="single"><h2>Description</h2>
<div><div>This function returns the adjacency matrix of the given graph <tt>G</tt>. The (i,j)<sup>th</sup> position of the matrix is 1 if there is an edge between the i<sup>th</sup> vertex and j<sup>th</sup> vertex, and 0 otherwise. The rows and columns are indexed by the variables of the ring and use the ordering of the variables for determining the order of the rows and columns.</div>
<table class="examples"><tr><td><pre>i1 : S = QQ[a..f];</pre>
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<tr><td><pre>i2 : G = graph {a*b,a*c,b*c,c*d,d*e,e*f,f*a,a*d}
o2 = Graph{edges => {{a, b}, {a, c}, {b, c}, {a, d}, {c, d}, {d, e}, {a, f}, {e, f}}}
ring => S
vertices => {a, b, c, d, e, f}
o2 : Graph</pre>
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<tr><td><pre>i3 : t = adjacencyMatrix G
o3 = | 0 1 1 1 0 1 |
| 1 0 1 0 0 0 |
| 1 1 0 1 0 0 |
| 1 0 1 0 1 0 |
| 0 0 0 1 0 1 |
| 1 0 0 0 1 0 |
6 6
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 : G = graph {a*b,a*c,b*c,c*d,d*e,e*f,f*a,a*d}
o5 = Graph{edges => {{f, e}, {e, d}, {d, c}, {c, b}, {f, a}, {d, a}, {c, a}, {b, a}}}
ring => T
vertices => {f, e, d, c, b, a}
o5 : Graph</pre>
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<tr><td><pre>i6 : t = adjacencyMatrix G -- although the same graph, matrix is different since variables have different ordering
o6 = | 0 1 0 0 0 1 |
| 1 0 1 0 0 0 |
| 0 1 0 1 0 1 |
| 0 0 1 0 1 1 |
| 0 0 0 1 0 1 |
| 1 0 1 1 1 0 |
6 6
o6 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_incidence__Matrix.html" title="returns the incidence matrix of a hypergraph">incidenceMatrix</a> -- returns the incidence matrix of a hypergraph</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>
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<div class="waystouse"><h2>Ways to use <tt>adjacencyMatrix</tt> :</h2>
<ul><li>adjacencyMatrix(Graph)</li>
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