- 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

- 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
- 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