# Graph

## Functions and methods returning an object of class 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), see diameter -- 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
• mixedGraph(Graph,Digraph) (missing documentation)
• mixedGraph(Graph,Digraph,Bigraph) (missing documentation)
• 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