Macaulay2 » Documentation
Packages » Graphs :: Graph
next | previous | forward | backward | up | index | toc

Graph

Functions and methods returning a graph:

  • addEdge(Digraph,Set) -- see addEdge -- A method for adding edges to a graph
  • addEdges'(Graph,List) (missing documentation)
  • addVertices(Digraph,List) -- see addVertex -- A method for adding a set of vertices to a graph
  • addVertices(Graph,List) (missing documentation)
  • barbellGraph(ZZ) -- see barbellGraph -- Returns the barbell graph
  • barycenter(Graph) -- see barycenter -- Returns the barycenter of a grah
  • cartesianProduct(Graph,Graph) -- see cartesianProduct -- Computes the cartesian product of two graphs
  • circularLadder(ZZ) -- see circularLadder -- Returns a circular ladder graph
  • cocktailParty(ZZ) -- see cocktailParty -- Returns a cocktail party graph
  • complementGraph(Graph) -- see complementGraph -- Returns the complement of a graph
  • completeGraph(ZZ) -- see completeGraph -- Constructs a complete graph
  • completeMultipartiteGraph(List) -- see completeMultipartiteGraph -- constructs a complete multipartite graph
  • crownGraph(ZZ) -- see crownGraph -- Returns a crown graph
  • cycleGraph(ZZ) -- see cycleGraph -- Constructs a cycle graph
  • deleteEdges(Graph,List) -- see deleteEdges -- Deletes a list of edges from a graph
  • deleteEdges(Digraph,List) (missing documentation)
  • deleteVertex(Graph,Thing) -- see deleteVertex -- a method for deleting the vertex of a graph
  • directProduct(Graph,Graph) -- see directProduct -- Computes the direct product of two graphs
  • disjointUnion(List) -- see disjointUnion -- Returns the disjoint union of a list of graphs.
  • doubleStar(ZZ,ZZ) -- see doubleStar -- returns a double star graph
  • friendshipGraph(ZZ) -- see friendshipGraph -- Returns a friendship Graph
  • generalizedPetersenGraph(ZZ,ZZ) -- see generalizedPetersenGraph -- Returns a generalized petersen graph
  • graph(HashTable) -- see graph -- Constructs a simple graph
  • graph(List) -- see graph -- Constructs a simple graph
  • graph(List,List) -- see graph -- Constructs a simple graph
  • graph(List,Matrix) -- see graph -- Constructs a simple graph
  • graph(Matrix) -- see graph -- Constructs a simple graph
  • graphComposition(Graph,Graph) -- see graphComposition -- A method for composing two graphs
  • graphLibrary(String) -- see graphLibrary -- constructs a graph of a type specified in the string input
  • graphPower(Graph,ZZ) -- see graphPower -- constructs a graph raised to a power
  • indexLabelGraph(Graph) -- see indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
  • inducedSubgraph(Graph,List) -- see inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
  • kneserGraph(ZZ,ZZ) -- see kneserGraph -- constructs a kneser graph of specified size
  • ladderGraph(ZZ) -- see ladderGraph -- Returns a ladder graph
  • lineGraph(Graph) -- see lineGraph -- Returns the line graph of an undirected graph
  • lollipopGraph(ZZ,ZZ) -- see lollipopGraph -- constructs a lollipop graph
  • monomialGraph(MonomialIdeal,ZZ) -- see monomialGraph -- Returns a monomial graph
  • pathGraph(ZZ) -- see pathGraph -- A method that makes a path graph
  • rattleGraph(ZZ,ZZ) -- see rattleGraph -- Returns a rattle graph
  • reindexBy(Graph,String) -- see reindexBy -- reindexes the vertices according to the input ordering.
  • spanningForest(Graph) -- see spanningForest -- constructs a spanning forest of a graph
  • starGraph(ZZ) -- see starGraph -- Returns a star graph
  • strongProduct(Graph,Graph) -- see strongProduct -- a method for taking the strong product of two graphs
  • thresholdGraph(List) -- see thresholdGraph -- A method that generates a threshold graph from a binary list
  • underlyingGraph(Digraph) -- see underlyingGraph -- Returns the underlying graph of a digraph
  • vertexMultiplication(Graph,Thing,Thing) -- see vertexMultiplication
  • wheelGraph(ZZ) -- see wheelGraph -- Constructs a wheel graph
  • windmillGraph(ZZ,ZZ) -- see windmillGraph -- Constructs a windmill graph

Methods that use a graph:

  • bipartiteColoring(Graph) -- see bipartiteColoring -- Returns a coloring of a bipartite graph
  • center(Graph) -- see center -- Returns the center of a graph
  • chromaticNumber(Graph) -- see chromaticNumber -- Computes the chromatic number of a graph
  • cliqueComplex(Graph) -- see cliqueComplex -- Returns the clique complex of a graph
  • cliqueNumber(Graph) -- see cliqueNumber -- Returns the clique number of a graph
  • closedNeighborhood(Graph,Thing) -- see closedNeighborhood -- Returns the closed neighborhood of a vertex of a graph
  • clusteringCoefficient(Graph) -- see clusteringCoefficient -- a method for computing the clustering coefficient of a Graph
  • clusteringCoefficient(Graph,Thing) -- see clusteringCoefficient -- a method for computing the clustering coefficient of a Graph
  • connectedComponents(Graph) -- Computes the connected components of a graph
  • coverIdeal(Graph) -- see coverIdeal -- Returns the vertex cover ideal of a graph
  • criticalEdges(Graph) -- see criticalEdges -- Finds the critical edges of a graph
  • degeneracy(Graph) -- see degeneracy -- Computes the degeneracy of a graph
  • degree(Graph,Thing) (missing documentation)
  • degreeCentrality(Graph,Thing) -- see degreeCentrality -- Returns the degreeCentrality of a vertex of a graph
  • degreeSequence(Graph) -- see degreeSequence -- the degree sequence of a graph
  • density(Graph) -- see density -- computes the density of a graph
  • diameter(Graph) -- Computes the diameter of a graph
  • eccentricity(Graph,Thing) -- see eccentricity -- Returns the eccentricity of a vertex of a graph
  • edgeConnectivity(Graph) -- see edgeConnectivity -- computes the edge connectivity of a graph
  • edgeCuts(Graph) -- see edgeCuts -- returns the edge cuts of a graph
  • edgeIdeal(Graph) -- see edgeIdeal -- returns the edge ideal of a graph
  • edges(Graph) -- see edges -- Returns the edges of a digraph or graph
  • expansion(Graph) -- see expansion -- returns the expansion of a graph
  • girth(Graph) -- see girth -- A method for computing the girth of a graph
  • hasEulerianTrail(Graph) -- see hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
  • hasOddHole(Graph) -- see hasOddHole -- checks whether a graph has a odd hole
  • incidenceMatrix(Graph) -- see incidenceMatrix -- computes the incidence matrix of a graph
  • independenceComplex(Graph) -- see independenceComplex -- constructs the independence complex of a graph
  • independenceNumber(Graph) -- see independenceNumber -- computes the independence number of a graph
  • isBipartite(Graph) -- see isBipartite -- determines whether a graph is bipartite
  • isChordal(Graph) -- see isChordal -- checks whether a graph is chordal
  • isCM(Graph) -- see isCM -- determines if a graph is Cohen-Macaulay
  • isConnected(Graph) -- see isConnected -- determines whether a graph is connected
  • isCyclic(Graph) -- see isCyclic -- determines whether a graph is cyclic
  • isEulerian(Graph) -- see isEulerian -- determines if a graph or digraph is Eulerian
  • isForest(Graph) -- see isForest -- determines whether a graph is a forest
  • isLeaf(Graph,Thing) -- see isLeaf -- determines whether a vertex is a leaf
  • isPerfect(Graph) -- see isPerfect -- checks whether a graph is perfect
  • isRegular(Graph) -- see isRegular -- determines whether a graph is regular
  • isRigid(Graph) -- see isRigid -- checks if a graph is rigid
  • isSimple(Graph) -- see isSimple -- checks if a graph is simple
  • isTree(Graph) -- see isTree -- determines whether a graph is a tree
  • laplacianMatrix(Graph) -- see laplacianMatrix -- Returns the laplacian matrix of a graph
  • leaves(Graph) -- see leaves -- lists the leaves of a tree graph
  • minimalDegree(Graph) -- see minimalDegree -- computes the minimal degree of a graph
  • minimalVertexCuts(Graph) -- see minimalVertexCuts -- finds the minimal vertex cuts of a graph
  • neighbors(Graph,Thing) -- see neighbors -- returns the neighbors of a vertex in a graph
  • nonneighbors(Graph,Thing) -- see nonneighbors -- returns the non-neighbors of a vertex in a graph
  • numberOfComponents(Graph) -- see numberOfComponents -- computes the number of connected components of a graph
  • numberOfTriangles(Graph) -- see numberOfTriangles -- counts how many subtriangles are present in a graph
  • radius(Graph) -- see radius -- Returns the radius of a graph
  • spectrum(Graph) -- see spectrum -- Returns the spectrum of a graph
  • vertexConnectivity(Graph) -- see vertexConnectivity -- computes the vertex connectivity of a graph
  • vertexCoverNumber(Graph) -- see vertexCoverNumber -- returns the vertex cover number of a graph
  • vertexCovers(Graph) -- see vertexCovers -- returns a list of the minimal vertex covers of a graph
  • vertexCuts(Graph) -- see vertexCuts -- lists all the vertex cuts of a graph
  • writeDotFile(String,Graph) -- see writeDotFile -- Writes a graph to a dot file with a specified filename

For the programmer

The object Graph is a type, with ancestor classes Digraph < HashTable < Thing.


The source of this document is in Graphs.m2:1775:0.