# Graph

## Functions and methods returning an object of class Graph :

• "addVertices(Digraph,List)" -- see addVertex -- A method for adding a set of vertices to a graph
• "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
• "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
• "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 an object of class 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) (missing documentation)
• clusteringCoefficient(Graph,Thing) (missing documentation)
• "connectedComponents(Graph)" -- see connectedComponents -- 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
• "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