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<head><title>getCliques -- returns cliques in a graph</title>
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<div><h1>getCliques -- returns cliques in 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>C = getCliques(G,d)</tt><br/><tt>C = getCliques 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>
<li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, representing the size of the cliques desired</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of cliques of size <tt>d</tt> or, if no <tt>d</tt> is entered, all cliques</span></li>
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<div class="single"><h2>Description</h2>
<div><div>A clique of a graph is a subset of its vertices which induces a complete subgraph. That is, a set of vertices is a clique if every pair of vertices in the set forms an edge of the graph. This function returns all cliques of a specified size, and if no size is given, it returns all cliques. Note that all the edges of the graph are considered cliques of size two.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : G = completeGraph R
o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}}
ring => R
vertices => {a, b, c, d}
o2 : Graph</pre>
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<tr><td><pre>i3 : getCliques(G,3)
o3 = {{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}}
o3 : List</pre>
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<tr><td><pre>i4 : getCliques(G,4)
o4 = {{a, b, c, d}}
o4 : List</pre>
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<tr><td><pre>i5 : getCliques G
o5 = {{a, b}, {a, c}, {b, c}, {a, d}, {b, d}, {c, d}, {a, b, c}, {a, b, d},
------------------------------------------------------------------------
{a, c, d}, {b, c, d}, {a, b, c, d}}
o5 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_clique__Number.html" title="computes the clique number of a graph">cliqueNumber</a> -- computes the clique number of a graph</span></li>
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<div class="waystouse"><h2>Ways to use <tt>getCliques</tt> :</h2>
<ul><li>getCliques(Graph)</li>
<li>getCliques(Graph,ZZ)</li>
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