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.