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<head><title>cycle -- returns a graph cycle</title>
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<div><h1>cycle -- returns a graph cycle</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>C = cycle R</tt><br/><tt>C = cycle(R,n)</tt><br/><tt>C = cycle L</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, length of cycle</span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of vertices to make into a cycle in the order provided</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Graph.html">graph</a></span>, a cycle on the vertices in <tt>L</tt> or on the variables of <tt>R</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Give a list of vertices (perhaps in some specified order), this function returns the graph of the cycle on those vertices, using the order given or the internal ordering of the <a href="_vertices.html" title="gets the vertices of a (hyper)graph">vertices</a>. Unspecified vertices are treated as isolated vertices.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a,b,c,d,e];</pre>
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<tr><td><pre>i2 : cycle R
o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}, {a, e}}}
ring => R
vertices => {a, b, c, d, e}
o2 : Graph</pre>
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<tr><td><pre>i3 : cycle(R,3)
o3 = Graph{edges => {{a, b}, {b, c}, {a, c}}}
ring => R
vertices => {a, b, c, d, e}
o3 : Graph</pre>
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<tr><td><pre>i4 : cycle {e,c,d,b}
o4 = Graph{edges => {{c, e}, {c, d}, {b, d}, {b, e}}}
ring => R
vertices => {a, b, c, d, e}
o4 : Graph</pre>
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<tr><td><pre>i5 : R = QQ[a,c,d,b,e];-- variables given different order</pre>
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<tr><td><pre>i6 : cycle R
o6 = Graph{edges => {{a, c}, {c, d}, {d, b}, {b, e}, {a, e}}}
ring => R
vertices => {a, c, d, b, e}
o6 : Graph</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_anti__Cycle.html" title="returns a graph of an anticycle">antiCycle</a> -- returns a graph of an anticycle</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>cycle</tt> :</h2>
<ul><li>cycle(List)</li>
<li>cycle(Ring)</li>
<li>cycle(Ring,ZZ)</li>
</ul>
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