- "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)" -- 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