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<!DOCTYPE html> <html lang="en"> <head> <title>EdgeIdeals : Table of Contents</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="A package for working with the edge ideals of (hyper)graphs" href="index.html">EdgeIdeals</a> :: <a href="toc.html">Table of Contents</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>EdgeIdeals : Table of Contents</h1> <ul> <li><span><a title="A package for working with the edge ideals of (hyper)graphs" href="index.html">EdgeIdeals</a> -- A package for working with the edge ideals of (hyper)graphs</span></li> <li><span><a title="returns the adjacency Matrix of a graph" href="_adjacency__Matrix.html">adjacencyMatrix</a> -- returns the adjacency Matrix of a graph</span></li> <li><span><a title="returns all even holes in a graph" href="_all__Even__Holes.html">allEvenHoles</a> -- returns all even holes in a graph</span></li> <li><span><a title="returns all odd holes in a graph" href="_all__Odd__Holes.html">allOddHoles</a> -- returns all odd holes in a graph</span></li> <li><span><a title="returns a graph of an anticycle" href="_anti__Cycle.html">antiCycle</a> -- returns a graph of an anticycle</span></li> <li><span><a title="optional argument for randomHyperGraph" href="___Branch__Limit.html">BranchLimit</a> -- optional argument for randomHyperGraph</span></li> <li><span><a title="replaces vertices with variables of a different ring" href="_change__Ring.html">changeRing</a> -- replaces vertices with variables of a different ring</span></li> <li><span><a title="optional argument for changeRing" href="_change__Ring_lp..._cm__Maximal__Edges_eq_gt..._rp.html">changeRing(...,MaximalEdges=>...)</a> -- optional argument for changeRing</span></li> <li><span><a title="computes the chromatic number of a hypergraph" href="_chromatic__Number.html">chromaticNumber</a> -- computes the chromatic number of a hypergraph</span></li> <li><span><a title="returns the clique complex of a graph" href="_clique__Complex.html">cliqueComplex</a> -- returns the clique complex of a graph</span></li> <li><span><a title="computes the clique number of a graph" href="_clique__Number.html">cliqueNumber</a> -- computes the clique number of a graph</span></li> <li><span><a title="returns the complement of a graph or hypergraph" href="_complement__Graph.html">complementGraph</a> -- returns the complement of a graph or hypergraph</span></li> <li><span><a title="returns a complete graph" href="_complete__Graph.html">completeGraph</a> -- returns a complete graph</span></li> <li><span><a title="returns a complete multipartite graph" href="_complete__Multi__Partite.html">completeMultiPartite</a> -- returns a complete multipartite graph</span></li> <li><span><a title="clarifying the difference between graph and hypergraph components" href="___Connected_sp__Components_sp__Tutorial.html">Connected Components Tutorial</a> -- clarifying the difference between graph and hypergraph components</span></li> <li><span><a title="returns the connected components of a hypergraph" href="_connected__Components.html">connectedComponents</a> -- returns the connected components of a hypergraph</span></li> <li><span><a title="returns the connected components of a graph" href="_connected__Graph__Components.html">connectedGraphComponents</a> -- returns the connected components of a graph</span></li> <li><span><a title="a summary of the many ways of making graphs and hypergraphs" href="___Constructor_sp__Overview.html">Constructor Overview</a> -- a summary of the many ways of making graphs and hypergraphs</span></li> <li><span><a title="creates the cover ideal of a (hyper)graph" href="_cover__Ideal.html">coverIdeal</a> -- creates the cover ideal of a (hyper)graph</span></li> <li><span><a title="returns a graph cycle" href="_cycle.html">cycle</a> -- returns a graph cycle</span></li> <li><span><a title="returns the degree of a vertex" href="_degree__Vertex.html">degreeVertex</a> -- returns the degree of a vertex</span></li> <li><span><a title="returns the (hyper)graph with specified edges removed" href="_delete__Edges.html">deleteEdges</a> -- returns the (hyper)graph with specified edges removed</span></li> <li><span><a title="creates the edge ideal of a (hyper)graph" href="_edge__Ideal.html">edgeIdeal</a> -- creates the edge ideal of a (hyper)graph</span></li> <li><span><a title="gets the edges of a (hyper)graph" href="_edges.html">edges</a> -- gets the edges of a (hyper)graph</span></li> <li><span><a title="an extended example using EdgeIdeals" href="___Extended_sp__Example.html">Extended Example</a> -- an extended example using EdgeIdeals</span></li> <li><span><a title="returns cliques in a graph" href="_get__Cliques.html">getCliques</a> -- returns cliques in a graph</span></li> <li><span><a title="gets the n-th edge in a (hyper)graph" href="_get__Edge.html">getEdge</a> -- gets the n-th edge in a (hyper)graph</span></li> <li><span><a title="finds the index of an edge in a HyperGraph" href="_get__Edge__Index.html">getEdgeIndex</a> -- finds the index of an edge in a HyperGraph</span></li> <li><span><a title="returns an edge that is a good leaf" href="_get__Good__Leaf.html">getGoodLeaf</a> -- returns an edge that is a good leaf</span></li> <li><span><a title="returns the index of an edge that is a good leaf" href="_get__Good__Leaf__Index.html">getGoodLeafIndex</a> -- returns the index of an edge that is a good leaf</span></li> <li><span><a title="returns maximal cliques in a graph" href="_get__Max__Cliques.html">getMaxCliques</a> -- returns maximal cliques in a graph</span></li> <li><span><a title="optional argument for isSCM" href="___Gins.html">Gins</a> -- optional argument for isSCM</span></li> <li><span><a title="a class for graphs" href="___Graph.html">Graph</a> -- a class for graphs</span></li> <li><span><a title="constructor for Graph" href="_graph.html">graph</a> -- constructor for Graph</span></li> <li><span><a title="determines if a HyperGraph contains a good leaf" href="_has__Good__Leaf.html">hasGoodLeaf</a> -- determines if a HyperGraph contains a good leaf</span></li> <li><span><a title="tells whether a graph contains an odd hole" href="_has__Odd__Hole.html">hasOddHole</a> -- tells whether a graph contains an odd hole</span></li> <li><span><a title="a class for hypergraphs" href="___Hyper__Graph.html">HyperGraph</a> -- a class for hypergraphs</span></li> <li><span><a title="constructor for HyperGraph" href="_hyper__Graph.html">hyperGraph</a> -- constructor for HyperGraph</span></li> <li><span><a title="equality" href="___Hyper__Graph_sp_eq_eq_sp__Hyper__Graph.html">HyperGraph == HyperGraph</a> -- equality</span></li> <li><span><a title="makes a simplicial complex from a (hyper)graph" href="_hyper__Graph__To__Simplicial__Complex.html">hyperGraphToSimplicialComplex</a> -- makes a simplicial complex from a (hyper)graph</span></li> <li><span><a title="returns the incidence matrix of a hypergraph" href="_incidence__Matrix.html">incidenceMatrix</a> -- returns the incidence matrix of a hypergraph</span></li> <li><span><a title="returns the independence complex of a (hyper)graph" href="_independence__Complex.html">independenceComplex</a> -- returns the independence complex of a (hyper)graph</span></li> <li><span><a title="determines the independence number of a graph" href="_independence__Number.html">independenceNumber</a> -- determines the independence number of a graph</span></li> <li><span><a title="returns the induced subgraph of a graph" href="_induced__Graph.html">inducedGraph</a> -- returns the induced subgraph of a graph</span></li> <li><span><a title="use OriginalRing inside inducedGraph or inducedHyperGraph" href="_induced__Graph_lp..._cm__Original__Ring_eq_gt..._rp.html">inducedGraph(...,OriginalRing=>...)</a> -- use OriginalRing inside inducedGraph or inducedHyperGraph</span></li> <li><span><a title="returns the induced subgraph of a (hyper)graph" href="_induced__Hyper__Graph.html">inducedHyperGraph</a> -- returns the induced subgraph of a (hyper)graph</span></li> <li><span><a title="determines if a graph is bipartite" href="_is__Bipartite.html">isBipartite</a> -- determines if a graph is bipartite</span></li> <li><span><a title="determines if a graph is chordal" href="_is__Chordal.html">isChordal</a> -- determines if a graph is chordal</span></li> <li><span><a title="determines if a (hyper)graph is Cohen-Macaulay" href="_is__C__M.html">isCM</a> -- determines if a (hyper)graph is Cohen-Macaulay</span></li> <li><span><a title="determines if a (hyper)graph is connected" href="_is__Connected.html">isConnected</a> -- determines if a (hyper)graph is connected</span></li> <li><span><a title="determines if a graph is connected" href="_is__Connected__Graph.html">isConnectedGraph</a> -- determines if a graph is connected</span></li> <li><span><a title="determines if an edge is in a (hyper)graph" href="_is__Edge.html">isEdge</a> -- determines if an edge is in a (hyper)graph</span></li> <li><span><a title="determines whether a (hyper)graph is a forest" href="_is__Forest.html">isForest</a> -- determines whether a (hyper)graph is a forest</span></li> <li><span><a title="determines if an edge is a good leaf" href="_is__Good__Leaf.html">isGoodLeaf</a> -- determines if an edge is a good leaf</span></li> <li><span><a title="determines if a hypergraph is a graph" href="_is__Graph.html">isGraph</a> -- determines if a hypergraph is a graph</span></li> <li><span><a title="determines if an edge (or vertex) is a leaf of a (hyper)graph" href="_is__Leaf.html">isLeaf</a> -- determines if an edge (or vertex) is a leaf of a (hyper)graph</span></li> <li><span><a title="returns all vertices not contained in any edge" href="_isolated__Vertices.html">isolatedVertices</a> -- returns all vertices not contained in any edge</span></li> <li><span><a title="determines whether a graph is perfect" href="_is__Perfect.html">isPerfect</a> -- determines whether a graph is perfect</span></li> <li><span><a title="determines if a (hyper)graph is sequentially Cohen-Macaulay" href="_is__S__C__M.html">isSCM</a> -- determines if a (hyper)graph is sequentially Cohen-Macaulay</span></li> <li><span><a title="use gins inside isSCM" href="_is__S__C__M_lp..._cm__Gins_eq_gt..._rp.html">isSCM(...,Gins=>...)</a> -- use gins inside isSCM</span></li> <li><span><a title="returns the line graph of a (hyper)graph" href="_line__Graph.html">lineGraph</a> -- returns the line graph of a (hyper)graph</span></li> <li><span><a title="optional argument for changeRing" href="___Maximal__Edges.html">MaximalEdges</a> -- optional argument for changeRing</span></li> <li><span><a title="returns the neighbors of a vertex or list of vertices" href="_neighbors.html">neighbors</a> -- returns the neighbors of a vertex or list of vertices</span></li> <li><span><a title="returns the number of connected components in a (hyper)graph" href="_num__Connected__Components.html">numConnectedComponents</a> -- returns the number of connected components in a (hyper)graph</span></li> <li><span><a title="returns the number of connected components in a graph" href="_num__Connected__Graph__Components.html">numConnectedGraphComponents</a> -- returns the number of connected components in a graph</span></li> <li><span><a title="returns the number of triangles in a graph" href="_num__Triangles.html">numTriangles</a> -- returns the number of triangles in a graph</span></li> <li><span><a title="optional argument for inducedHyperGraph" href="___Original__Ring.html">OriginalRing</a> -- optional argument for inducedHyperGraph</span></li> <li><span><a title="returns a random graph" href="_random__Graph.html">randomGraph</a> -- returns a random graph</span></li> <li><span><a title="returns a random hypergraph" href="_random__Hyper__Graph.html">randomHyperGraph</a> -- returns a random hypergraph</span></li> <li><span><a title="limit recursive branching in randomHyperGraph" href="_random__Hyper__Graph_lp..._cm__Branch__Limit_eq_gt..._rp.html">randomHyperGraph(...,BranchLimit=>...)</a> -- limit recursive branching in randomHyperGraph</span></li> <li><span><a title="limit the running time of randomHyperGraph" href="_random__Hyper__Graph_lp..._cm__Time__Limit_eq_gt..._rp.html">randomHyperGraph(...,TimeLimit=>...)</a> -- limit the running time of randomHyperGraph</span></li> <li><span><a title="returns a random uniform hypergraph" href="_random__Uniform__Hyper__Graph.html">randomUniformHyperGraph</a> -- returns a random uniform hypergraph</span></li> <li><span><a title="gives the ring of a (hyper)graph" href="_ring_lp__Hyper__Graph_rp.html">ring(HyperGraph)</a> -- gives the ring of a (hyper)graph</span></li> <li><span><a title="makes a (hyper)graph from a simplicial complex" href="_simplicial__Complex__To__Hyper__Graph.html">simplicialComplexToHyperGraph</a> -- makes a (hyper)graph from a simplicial complex</span></li> <li><span><a title="returns the size of the smallest induced cycle of a graph" href="_smallest__Cycle__Size.html">smallestCycleSize</a> -- returns the size of the smallest induced cycle of a graph</span></li> <li><span><a title="returns a spanning tree of a graph" href="_spanning__Tree.html">spanningTree</a> -- returns a spanning tree of a graph</span></li> <li><span><a title="optional argument for randomHyperGraph" href="___Time__Limit.html">TimeLimit</a> -- optional argument for randomHyperGraph</span></li> <li><span><a title="find the vertex covering number of a (hyper)graph" href="_vertex__Cover__Number.html">vertexCoverNumber</a> -- find the vertex covering number of a (hyper)graph</span></li> <li><span><a title="list the minimal vertex covers of a (hyper)graph" href="_vertex__Covers.html">vertexCovers</a> -- list the minimal vertex covers of a (hyper)graph</span></li> <li><span><a title="gets the vertices of a (hyper)graph" href="_vertices_lp__Hyper__Graph_rp.html">vertices(HyperGraph)</a> -- gets the vertices of a (hyper)graph</span></li> </ul> </body> </html>