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<div><h1>HyperGraph -- a class for hypergraphs</h1>
<div class="single"><h2>Description</h2>
<div><div>This class represents hypergraphs. A hypergraph is a tuple <tt>(V,E)</tt> of vertices <tt>V</tt> and edges <tt>E</tt> which are subsets of the vertices. In this package, all hypergraphs have the additional property that no edge is a subset of any other edge. Hypergraphs of this form are often referred to as clutters.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[w,x,y,z];</pre>
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<tr><td><pre>i2 : H = hyperGraph(R, {{w,x},{w,y,z},{x,y,z}});</pre>
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<tr><td><pre>i3 : vertices H
o3 = {w, x, y, z}
o3 : List</pre>
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<tr><td><pre>i4 : edges H
o4 = {{w, x}, {w, y, z}, {x, y, z}}
o4 : List</pre>
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<tr><td><pre>i5 : ring H
o5 = R
o5 : PolynomialRing</pre>
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<div>Hypergraphs are always associated with a polynomial ring whose variables are the vertices of the hypergraph.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></li>
<li><span><a href="___Graph.html" title="a class for graphs">Graph</a> -- a class for graphs</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>
</ul>
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<div class="waystouse"><h2>Types of hypergraph :</h2>
<ul><li><span><a href="___Graph.html" title="a class for graphs">Graph</a> -- a class for graphs</span></li>
</ul>
<h2>Functions and methods returning a hypergraph :</h2>
<ul><li><span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></li>
<li><span>hyperGraph(Graph), see <span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></span></li>
<li><span>hyperGraph(Ideal), see <span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></span></li>
<li><span>hyperGraph(List), see <span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></span></li>
<li><span>hyperGraph(MonomialIdeal), see <span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></span></li>
<li><span>hyperGraph(PolynomialRing,List), see <span><a href="_hyper__Graph.html" title="constructor for HyperGraph">hyperGraph</a> -- constructor for HyperGraph</span></span></li>
</ul>
<h2>Methods that use a hypergraph :</h2>
<ul><li><span>changeRing(HyperGraph,PolynomialRing,List), see <span><a href="_change__Ring.html" title="replaces vertices with variables of a different ring">changeRing</a> -- replaces vertices with variables of a different ring</span></span></li>
<li><span>chromaticNumber(HyperGraph), see <span><a href="_chromatic__Number.html" title="computes the chromatic number of a hypergraph">chromaticNumber</a> -- computes the chromatic number of a hypergraph</span></span></li>
<li><span>complementGraph(HyperGraph), see <span><a href="_complement__Graph.html" title="returns the complement of a graph or hypergraph">complementGraph</a> -- returns the complement of a graph or hypergraph</span></span></li>
<li><span>connectedComponents(HyperGraph), see <span><a href="_connected__Components.html" title="returns the connected components of a hypergraph">connectedComponents</a> -- returns the connected components of a hypergraph</span></span></li>
<li><span>connectedGraphComponents(HyperGraph), see <span><a href="_connected__Graph__Components.html" title="returns the connected components of a graph">connectedGraphComponents</a> -- returns the connected components of a graph</span></span></li>
<li><span>coverIdeal(HyperGraph), see <span><a href="_cover__Ideal.html" title="creates the cover ideal of a (hyper)graph">coverIdeal</a> -- creates the cover ideal of a (hyper)graph</span></span></li>
<li><span>degreeVertex(HyperGraph,RingElement), see <span><a href="_degree__Vertex.html" title="returns the degree of a vertex">degreeVertex</a> -- returns the degree of a vertex</span></span></li>
<li><span>degreeVertex(HyperGraph,ZZ), see <span><a href="_degree__Vertex.html" title="returns the degree of a vertex">degreeVertex</a> -- returns the degree of a vertex</span></span></li>
<li><span>deleteEdges(HyperGraph,List), see <span><a href="_delete__Edges.html" title="returns the (hyper)graph with specified edges removed">deleteEdges</a> -- returns the (hyper)graph with specified edges removed</span></span></li>
<li><span>edgeIdeal(HyperGraph), see <span><a href="_edge__Ideal.html" title="creates the edge ideal of a (hyper)graph">edgeIdeal</a> -- creates the edge ideal of a (hyper)graph</span></span></li>
<li><span>edges(HyperGraph), see <span><a href="_edges.html" title="gets the edges of a (hyper)graph">edges</a> -- gets the edges of a (hyper)graph</span></span></li>
<li><span>getEdge(HyperGraph,ZZ), see <span><a href="_get__Edge.html" title="gets the n-th edge in a (hyper)graph">getEdge</a> -- gets the n-th edge in a (hyper)graph</span></span></li>
<li><span>getEdgeIndex(HyperGraph,List), see <span><a href="_get__Edge__Index.html" title="finds the index of an edge in a HyperGraph">getEdgeIndex</a> -- finds the index of an edge in a HyperGraph</span></span></li>
<li><span>getEdgeIndex(HyperGraph,RingElement), see <span><a href="_get__Edge__Index.html" title="finds the index of an edge in a HyperGraph">getEdgeIndex</a> -- finds the index of an edge in a HyperGraph</span></span></li>
<li><span>getGoodLeaf(HyperGraph), see <span><a href="_get__Good__Leaf.html" title="returns an edge that is a good leaf">getGoodLeaf</a> -- returns an edge that is a good leaf</span></span></li>
<li><span>getGoodLeafIndex(HyperGraph), see <span><a href="_get__Good__Leaf__Index.html" title="returns the index of an edge that is a good leaf">getGoodLeafIndex</a> -- returns the index of an edge that is a good leaf</span></span></li>
<li><span>graph(HyperGraph), see <span><a href="_graph.html" title="constructor for Graph">graph</a> -- constructor for Graph</span></span></li>
<li><span>hasGoodLeaf(HyperGraph), see <span><a href="_has__Good__Leaf.html" title="determines if a HyperGraph contains a good leaf">hasGoodLeaf</a> -- determines if a HyperGraph contains a good leaf</span></span></li>
<li><span><a href="___Hyper__Graph_sp_eq_eq_sp__Hyper__Graph.html" title="equality">HyperGraph == HyperGraph</a> -- equality</span></li>
<li><span>hyperGraphToSimplicialComplex(HyperGraph), see <span><a href="_hyper__Graph__To__Simplicial__Complex.html" title="makes a simplicial complex from a (hyper)graph">hyperGraphToSimplicialComplex</a> -- makes a simplicial complex from a (hyper)graph</span></span></li>
<li><span>incidenceMatrix(HyperGraph), see <span><a href="_incidence__Matrix.html" title="returns the incidence matrix of a hypergraph">incidenceMatrix</a> -- returns the incidence matrix of a hypergraph</span></span></li>
<li><span>independenceComplex(HyperGraph), see <span><a href="_independence__Complex.html" title="returns the independence complex of a (hyper)graph">independenceComplex</a> -- returns the independence complex of a (hyper)graph</span></span></li>
<li><span>inducedHyperGraph(HyperGraph,List), see <span><a href="_induced__Hyper__Graph.html" title="returns the induced subgraph of a (hyper)graph">inducedHyperGraph</a> -- returns the induced subgraph of a (hyper)graph</span></span></li>
<li><span>isCM(HyperGraph), see <span><a href="_is__C__M.html" title="determines if a (hyper)graph is Cohen-Macaulay">isCM</a> -- determines if a (hyper)graph is Cohen-Macaulay</span></span></li>
<li><span>isConnected(HyperGraph), see <span><a href="_is__Connected.html" title="determines if a (hyper)graph is connected">isConnected</a> -- determines if a (hyper)graph is connected</span></span></li>
<li><span>isConnectedGraph(HyperGraph), see <span><a href="_is__Connected__Graph.html" title="determines if a graph is connected">isConnectedGraph</a> -- determines if a graph is connected</span></span></li>
<li><span>isEdge(HyperGraph,List), see <span><a href="_is__Edge.html" title="determines if an edge is in a (hyper)graph">isEdge</a> -- determines if an edge is in a (hyper)graph</span></span></li>
<li><span>isEdge(HyperGraph,RingElement), see <span><a href="_is__Edge.html" title="determines if an edge is in a (hyper)graph">isEdge</a> -- determines if an edge is in a (hyper)graph</span></span></li>
<li><span>isForest(HyperGraph), see <span><a href="_is__Forest.html" title="determines whether a (hyper)graph is a forest">isForest</a> -- determines whether a (hyper)graph is a forest</span></span></li>
<li><span>isGoodLeaf(HyperGraph,ZZ), see <span><a href="_is__Good__Leaf.html" title="determines if an edge is a good leaf">isGoodLeaf</a> -- determines if an edge is a good leaf</span></span></li>
<li><span>isGraph(HyperGraph), see <span><a href="_is__Graph.html" title="determines if a hypergraph is a graph">isGraph</a> -- determines if a hypergraph is a graph</span></span></li>
<li><span>isLeaf(HyperGraph,RingElement), see <span><a href="_is__Leaf.html" title="determines if an edge (or vertex) is a leaf of a (hyper)graph">isLeaf</a> -- determines if an edge (or vertex) is a leaf of a (hyper)graph</span></span></li>
<li><span>isLeaf(HyperGraph,ZZ), see <span><a href="_is__Leaf.html" title="determines if an edge (or vertex) is a leaf of a (hyper)graph">isLeaf</a> -- determines if an edge (or vertex) is a leaf of a (hyper)graph</span></span></li>
<li><span>isolatedVertices(HyperGraph), see <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></span></li>
<li><span>isSCM(HyperGraph), see <span><a href="_is__S__C__M.html" title="determines if a (hyper)graph is sequentially Cohen-Macaulay">isSCM</a> -- determines if a (hyper)graph is sequentially Cohen-Macaulay</span></span></li>
<li><span>lineGraph(HyperGraph), see <span><a href="_line__Graph.html" title="returns the line graph of a (hyper)graph">lineGraph</a> -- returns the line graph of a (hyper)graph</span></span></li>
<li><span>neighbors(HyperGraph,List), see <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></span></li>
<li><span>neighbors(HyperGraph,RingElement), see <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></span></li>
<li><span>neighbors(HyperGraph,ZZ), see <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></span></li>
<li><span>numConnectedComponents(HyperGraph), see <span><a href="_num__Connected__Components.html" title="returns the number of connected components in a (hyper)graph">numConnectedComponents</a> -- returns the number of connected components in a (hyper)graph</span></span></li>
<li><span>numConnectedGraphComponents(HyperGraph), see <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></span></li>
<li><span><a href="_ring_lp__Hyper__Graph_rp.html" title="gives the ring of a (hyper)graph">ring(HyperGraph)</a> -- gives the ring of a (hyper)graph</span></li>
<li><span>vertexCoverNumber(HyperGraph), see <span><a href="_vertex__Cover__Number.html" title="find the vertex covering number of a (hyper)graph">vertexCoverNumber</a> -- find the vertex covering number of a (hyper)graph</span></span></li>
<li><span>vertexCovers(HyperGraph), see <span><a href="_vertex__Covers.html" title="list the minimal vertex covers of a (hyper)graph">vertexCovers</a> -- list the minimal vertex covers of a (hyper)graph</span></span></li>
<li><span>vertices(HyperGraph), see <span><a href="_vertices.html" title="gets the vertices of a (hyper)graph">vertices</a> -- gets the vertices of a (hyper)graph</span></span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Hyper__Graph.html" title="a class for hypergraphs">HyperGraph</a> is <span>a <a href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a href="../../Macaulay2Doc/html/___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="../../Macaulay2Doc/html/___Thing.html" title="the class of all things">Thing</a>.</p>
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