EdgeIdeals : Table of Contents

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