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EdgeIdeals : Index
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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