EdgeIdeals : Index

• adjacencyMatrix -- returns the adjacency Matrix of a graph
• adjacencyMatrix(Graph) -- returns the adjacency Matrix of a graph
• allEvenHoles -- returns all even holes in a graph
• allEvenHoles(Graph) -- returns all even holes in a graph
• allOddHoles -- returns all odd holes in a graph
• allOddHoles(Graph) -- returns all odd holes in a graph
• antiCycle -- returns a graph of an anticycle
• antiCycle(List) -- returns a graph of an anticycle
• antiCycle(Ring) -- returns a graph of an anticycle
• antiCycle(Ring,ZZ) -- returns a graph of an anticycle
• BranchLimit -- optional argument for randomHyperGraph
• changeRing -- replaces vertices with variables of a different ring
• changeRing(...,MaximalEdges=>...) -- optional argument for changeRing
• changeRing(HyperGraph,PolynomialRing,List) -- replaces vertices with variables of a different ring
• chromaticNumber -- computes the chromatic number of a hypergraph
• chromaticNumber(HyperGraph) -- computes the chromatic number of a hypergraph
• cliqueComplex -- returns the clique complex of a graph
• cliqueComplex(Graph) -- returns the clique complex of a graph
• cliqueNumber -- computes the clique number of a graph
• cliqueNumber(Graph) -- computes the clique number of a graph
• complementGraph -- returns the complement of a graph or hypergraph
• complementGraph(Graph) -- returns the complement of a graph or hypergraph
• complementGraph(HyperGraph) -- returns the complement of a graph or hypergraph
• completeGraph -- returns a complete graph
• completeGraph(List) -- returns a complete graph
• completeGraph(Ring) -- returns a complete graph
• completeGraph(Ring,ZZ) -- returns a complete graph
• completeMultiPartite -- returns a complete multipartite graph
• completeMultiPartite(Ring,List) -- returns a complete multipartite graph
• completeMultiPartite(Ring,ZZ,ZZ) -- returns a complete multipartite graph
• Connected Components Tutorial -- clarifying the difference between graph and hypergraph components
• connectedComponents -- returns the connected components of a hypergraph
• connectedComponents(HyperGraph) -- returns the connected components of a hypergraph
• connectedGraphComponents -- returns the connected components of a graph
• connectedGraphComponents(HyperGraph) -- returns the connected components of a graph
• Constructor Overview -- a summary of the many ways of making graphs and hypergraphs
• coverIdeal -- creates the cover ideal of a (hyper)graph
• coverIdeal(HyperGraph) -- creates the cover ideal of a (hyper)graph
• cycle -- returns a graph cycle
• cycle(List) -- returns a graph cycle
• cycle(Ring) -- returns a graph cycle
• cycle(Ring,ZZ) -- returns a graph cycle
• degreeVertex -- returns the degree of a vertex
• degreeVertex(HyperGraph,RingElement) -- returns the degree of a vertex
• degreeVertex(HyperGraph,ZZ) -- returns the degree of a vertex
• deleteEdges -- returns the (hyper)graph with specified edges removed
• deleteEdges(HyperGraph,List) -- returns the (hyper)graph with specified edges removed
• edgeIdeal -- creates the edge ideal of a (hyper)graph
• edgeIdeal(HyperGraph) -- creates the edge ideal of a (hyper)graph
• EdgeIdeals -- A package for working with the edge ideals of (hyper)graphs
• edges -- gets the edges of a (hyper)graph
• edges(HyperGraph) -- gets the edges of a (hyper)graph
• Extended Example -- an extended example using EdgeIdeals
• getCliques -- returns cliques in a graph
• getCliques(Graph) -- returns cliques in a graph
• getCliques(Graph,ZZ) -- returns cliques in a graph
• getEdge -- gets the n-th edge in a (hyper)graph
• getEdge(HyperGraph,ZZ) -- gets the n-th edge in a (hyper)graph
• getEdgeIndex -- finds the index of an edge in a HyperGraph
• getEdgeIndex(HyperGraph,List) -- finds the index of an edge in a HyperGraph
• getEdgeIndex(HyperGraph,RingElement) -- finds the index of an edge in a HyperGraph
• getGoodLeaf -- returns an edge that is a good leaf
• getGoodLeaf(HyperGraph) -- returns an edge that is a good leaf
• getGoodLeafIndex -- returns the index of an edge that is a good leaf
• getGoodLeafIndex(HyperGraph) -- returns the index of an edge that is a good leaf
• getMaxCliques -- returns maximal cliques in a graph
• getMaxCliques(Graph) -- returns maximal cliques in a graph
• Gins -- optional argument for isSCM
• Graph -- a class for graphs
• graph -- constructor for Graph
• graph(HyperGraph) -- constructor for Graph
• graph(Ideal) -- constructor for Graph
• graph(List) -- constructor for Graph
• graph(MonomialIdeal) -- constructor for Graph
• graph(PolynomialRing,List) -- constructor for Graph
• hasGoodLeaf -- determines if a HyperGraph contains a good leaf
• hasGoodLeaf(HyperGraph) -- determines if a HyperGraph contains a good leaf
• hasOddHole -- tells whether a graph contains an odd hole
• hasOddHole(Graph) -- tells whether a graph contains an odd hole
• HyperGraph -- a class for hypergraphs
• hyperGraph -- constructor for HyperGraph
• HyperGraph == HyperGraph -- equality
• hyperGraph(Graph) -- constructor for HyperGraph
• hyperGraph(Ideal) -- constructor for HyperGraph
• hyperGraph(List) -- constructor for HyperGraph
• hyperGraph(MonomialIdeal) -- constructor for HyperGraph
• hyperGraph(PolynomialRing,List) -- constructor for HyperGraph
• hyperGraphToSimplicialComplex -- makes a simplicial complex from a (hyper)graph
• hyperGraphToSimplicialComplex(HyperGraph) -- makes a simplicial complex from a (hyper)graph
• incidenceMatrix -- returns the incidence matrix of a hypergraph
• incidenceMatrix(HyperGraph) -- returns the incidence matrix of a hypergraph
• independenceComplex -- returns the independence complex of a (hyper)graph
• independenceComplex(HyperGraph) -- returns the independence complex of a (hyper)graph
• independenceNumber -- determines the independence number of a graph
• independenceNumber(Graph) -- determines the independence number of a graph
• inducedGraph -- returns the induced subgraph of a graph
• inducedGraph(...,OriginalRing=>...) -- use OriginalRing inside inducedGraph or inducedHyperGraph
• inducedGraph(Graph,List) -- returns the induced subgraph of a graph
• inducedHyperGraph -- returns the induced subgraph of a (hyper)graph
• inducedHyperGraph(...,OriginalRing=>...) -- use OriginalRing inside inducedGraph or inducedHyperGraph
• inducedHyperGraph(HyperGraph,List) -- returns the induced subgraph of a (hyper)graph
• isBipartite -- determines if a graph is bipartite
• isBipartite(Graph) -- determines if a graph is bipartite
• isChordal -- determines if a graph is chordal
• isChordal(Graph) -- determines if a graph is chordal
• isCM -- determines if a (hyper)graph is Cohen-Macaulay
• isCM(HyperGraph) -- determines if a (hyper)graph is Cohen-Macaulay
• isConnected -- determines if a (hyper)graph is connected
• isConnected(HyperGraph) -- determines if a (hyper)graph is connected
• isConnectedGraph -- determines if a graph is connected
• isConnectedGraph(HyperGraph) -- determines if a graph is connected
• isEdge -- determines if an edge is in a (hyper)graph
• isEdge(HyperGraph,List) -- determines if an edge is in a (hyper)graph
• isEdge(HyperGraph,RingElement) -- determines if an edge is in a (hyper)graph
• isForest -- determines whether a (hyper)graph is a forest
• isForest(Graph) -- determines whether a (hyper)graph is a forest
• isForest(HyperGraph) -- determines whether a (hyper)graph is a forest
• isGoodLeaf -- determines if an edge is a good leaf
• isGoodLeaf(HyperGraph,ZZ) -- determines if an edge is a good leaf
• isGraph -- determines if a hypergraph is a graph
• isGraph(HyperGraph) -- determines if a hypergraph is a graph
• isLeaf -- determines if an edge (or vertex) is a leaf of a (hyper)graph
• isLeaf(Graph,ZZ) -- determines if an edge (or vertex) is a leaf of a (hyper)graph
• isLeaf(HyperGraph,RingElement) -- determines if an edge (or vertex) is a leaf of a (hyper)graph
• isLeaf(HyperGraph,ZZ) -- determines if an edge (or vertex) is a leaf of a (hyper)graph
• isolatedVertices -- returns all vertices not contained in any edge
• isolatedVertices(HyperGraph) -- returns all vertices not contained in any edge
• isPerfect -- determines whether a graph is perfect
• isPerfect(Graph) -- determines whether a graph is perfect
• isSCM -- determines if a (hyper)graph is sequentially Cohen-Macaulay
• isSCM(...,Gins=>...) -- use gins inside isSCM
• isSCM(HyperGraph) -- determines if a (hyper)graph is sequentially Cohen-Macaulay
• lineGraph -- returns the line graph of a (hyper)graph
• lineGraph(HyperGraph) -- returns the line graph of a (hyper)graph
• MaximalEdges -- optional argument for changeRing
• neighbors -- returns the neighbors of a vertex or list of vertices
• neighbors(HyperGraph,List) -- returns the neighbors of a vertex or list of vertices
• neighbors(HyperGraph,RingElement) -- returns the neighbors of a vertex or list of vertices
• neighbors(HyperGraph,ZZ) -- returns the neighbors of a vertex or list of vertices
• numConnectedComponents -- returns the number of connected components in a (hyper)graph
• numConnectedComponents(HyperGraph) -- returns the number of connected components in a (hyper)graph
• numConnectedGraphComponents -- returns the number of connected components in a graph
• numConnectedGraphComponents(HyperGraph) -- returns the number of connected components in a graph
• numTriangles -- returns the number of triangles in a graph
• numTriangles(Graph) -- returns the number of triangles in a graph
• OriginalRing -- optional argument for inducedHyperGraph
• randomGraph -- returns a random graph
• randomGraph(PolynomialRing,ZZ) -- returns a random graph
• randomHyperGraph -- returns a random hypergraph
• randomHyperGraph(...,BranchLimit=>...) -- limit recursive branching in randomHyperGraph
• randomHyperGraph(...,TimeLimit=>...) -- limit the running time of randomHyperGraph
• randomHyperGraph(PolynomialRing,List) -- returns a random hypergraph
• randomUniformHyperGraph -- returns a random uniform hypergraph
• randomUniformHyperGraph(PolynomialRing,ZZ,ZZ) -- returns a random uniform hypergraph
• ring(HyperGraph) -- gives the ring of a (hyper)graph
• simplicialComplexToHyperGraph -- makes a (hyper)graph from a simplicial complex
• simplicialComplexToHyperGraph(SimplicialComplex) -- makes a (hyper)graph from a simplicial complex
• smallestCycleSize -- returns the size of the smallest induced cycle of a graph
• smallestCycleSize(Graph) -- returns the size of the smallest induced cycle of a graph
• spanningTree -- returns a spanning tree of a graph
• spanningTree(Graph) -- returns a spanning tree of a graph
• TimeLimit -- optional argument for randomHyperGraph
• vertexCoverNumber -- find the vertex covering number of a (hyper)graph
• vertexCoverNumber(HyperGraph) -- find the vertex covering number of a (hyper)graph
• vertexCovers -- list the minimal vertex covers of a (hyper)graph
• vertexCovers(HyperGraph) -- list the minimal vertex covers of a (hyper)graph
• vertices(HyperGraph) -- gets the vertices of a (hyper)graph