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<head><title>connectedGraphComponents -- returns the connected components of a graph</title>
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<div><h1>connectedGraphComponents -- returns the connected components 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>L = connectedGraphComponents G</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</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>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of lists of vertices. Each list of vertices is a connected component of G.</span></li>
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<div class="single"><h2>Description</h2>
<div><p>This function returns the connected components of a graph. A connected component of a graph is any maximal set of vertices which are pairwise connected by a (possibly trivial) path. Isolated vertices, which are those not appearing in any edge, form their own connected components. This is in contrast to <a href="_connected__Components.html" title="returns the connected components of a hypergraph">connectedComponents</a> in which isolated vertices do not appear in any connected components. See the <a href="___Connected_sp__Components_sp__Tutorial.html" title="clarifying the difference between graph and hypergraph components">Connected Components Tutorial</a> for more information.</p>
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<table class="examples"><tr><td><pre>i1 : R = QQ[a..k];</pre>
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<tr><td><pre>i2 : G = graph {a*b,b*c,c*d,a*d,f*g,h*i,j*k,h*k}
o2 = Graph{edges => {{a, b}, {b, c}, {a, d}, {c, d}, {f, g}, {h, i}, {h, k}, {j, k}}}
ring => R
vertices => {a, b, c, d, e, f, g, h, i, j, k}
o2 : Graph</pre>
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<tr><td><pre>i3 : L = connectedGraphComponents G
o3 = {{e}, {a, b, c, d}, {f, g}, {h, i, j, k}}
o3 : List</pre>
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<p>In the following example, graph <tt>G</tt> contains the isolated vertex <tt>d</tt>. Notice that <tt>d</tt> appears in its own connected component and hence <tt>G</tt> is not connected.</p>
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<table class="examples"><tr><td><pre>i4 : R = QQ[a,b,c,d];</pre>
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<tr><td><pre>i5 : G = graph {a*b, b*c}
o5 = Graph{edges => {{a, b}, {b, c}}}
ring => R
vertices => {a, b, c, d}
o5 : Graph</pre>
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<tr><td><pre>i6 : connectedGraphComponents G
o6 = {{d}, {a, b, c}}
o6 : List</pre>
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<tr><td><pre>i7 : isolatedVertices G
o7 = {d}
o7 : List</pre>
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<tr><td><pre>i8 : isConnectedGraph G
o8 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Connected_sp__Components_sp__Tutorial.html" title="clarifying the difference between graph and hypergraph components">Connected Components Tutorial</a> -- clarifying the difference between graph and hypergraph components</span></li>
<li><span><a href="_connected__Components.html" title="returns the connected components of a hypergraph">connectedComponents</a> -- returns the connected components of a hypergraph</span></li>
<li><span><a href="_is__Connected__Graph.html" title="determines if a graph is connected">isConnectedGraph</a> -- determines if a graph is connected</span></li>
<li><span><a href="_num__Connected__Graph__Components.html" title="returns the number of connected components in a graph">numConnectedGraphComponents</a> -- returns the number of connected components in a graph</span></li>
<li><span><a href="_isolated__Vertices.html" title="returns all vertices not contained in any edge">isolatedVertices</a> -- returns all vertices not contained in any edge</span></li>
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<div class="waystouse"><h2>Ways to use <tt>connectedGraphComponents</tt> :</h2>
<ul><li>connectedGraphComponents(HyperGraph)</li>
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