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<head><title>degreeVertex -- returns the degree of a vertex</title>
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<div><h1>degreeVertex -- returns the degree of a vertex</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>d = degreeVertex(H,n)</tt><br/><tt>d = degreeVertex(H,V)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the index of a vertex</span></li>
<li><span><tt>V</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a vertex/variable of the HyperGraph</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the degree of vertex <tt>V</tt> (or vertex number <tt>n</tt>)</span></li>
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<div class="single"><h2>Description</h2>
<div><div>The degree of a vertex in a (hyper)graph is the number of edges that contain the vertex. In a graph, the degree is also the number of elements in the neighbor set of a vertex.</div>
<table class="examples"><tr><td><pre>i1 : S = QQ[a,b,c,d,e];</pre>
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<tr><td><pre>i2 : k5 = completeGraph S
o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}}
ring => S
vertices => {a, b, c, d, e}
o2 : Graph</pre>
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<tr><td><pre>i3 : dv = degreeVertex(k5,a)
o3 = 4</pre>
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<tr><td><pre>i4 : n = neighbors(k5,a)
o4 = {b, c, d, e}
o4 : List</pre>
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<tr><td><pre>i5 : #n == dv
o5 = true</pre>
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<tr><td><pre>i6 : degreeVertex(k5,2)
o6 = 4</pre>
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<tr><td><pre>i7 : h = hyperGraph {a*b*c,c*d,a*d*e,b*e,c*e}
o7 = HyperGraph{edges => {{a, b, c}, {c, d}, {b, e}, {c, e}, {a, d, e}}}
ring => S
vertices => {a, b, c, d, e}
o7 : HyperGraph</pre>
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<tr><td><pre>i8 : degreeVertex(h,a)
o8 = 2</pre>
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<tr><td><pre>i9 : degreeVertex(h,2) -- degree of c
o9 = 3</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_neighbors.html" title="returns the neighbors of a vertex or list of vertices">neighbors</a> -- returns the neighbors of a vertex or list of vertices</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>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>degreeVertex</tt> :</h2>
<ul><li>degreeVertex(HyperGraph,RingElement)</li>
<li>degreeVertex(HyperGraph,ZZ)</li>
</ul>
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