- addEdge -- A method for adding edges to a graph
- addVertex -- A method for adding a set of vertices to a graph
- adjacencyMatrix -- Returns the adjacency matrix of a Graph or Digraph
- barbellGraph -- Returns the barbell graph
- barycenter -- Returns the barycenter of a grah
`BFS`(missing documentation)`bigraph`(missing documentation)- bipartiteColoring -- Returns a coloring of a bipartite graph
- breadthFirstSearch -- runs a breadth first search on the digraph starting at a specified node and returns a list of the vertices in the order they were discovered
- cartesianProduct -- Computes the cartesian product of two graphs
- center -- Returns the center of a graph
- children -- returns the children of a vertex of a digraph
- chromaticNumber -- Computes the chromatic number of a graph
- circularLadder -- Returns a circular ladder graph
- cliqueComplex -- Returns the clique complex of a graph
- cliqueNumber -- Returns the clique number of a graph
- closedNeighborhood -- Returns the closed neighborhood of a vertex of a graph
`clusteringCoefficient`(missing documentation)- cocktailParty -- Returns a cocktail party graph
`collateVertices`(missing documentation)- complementGraph -- Returns the complement of a graph
- completeGraph -- Constructs a complete graph
- completeMultipartiteGraph -- constructs a complete multipartite graph
- connectedComponents -- Computes the connected components of a graph
- coverIdeal -- Returns the vertex cover ideal of a graph
- criticalEdges -- Finds the critical edges of a graph
- crownGraph -- Returns a crown graph
- cycleGraph -- Constructs a cycle graph
- degeneracy -- Computes the degeneracy of a graph
- degree(Digraph,Thing) -- returns the degree of a vertex in a digraph
- degreeCentrality -- Returns the degreeCentrality of a vertex of a graph
- degreeIn -- returns the "in-degree" of a vertex in a digraph
- degreeMatrix -- Returns the degree matrix of a graph
- degreeOut -- returns the "out-degree" of a vertex in a digraph
- deleteEdges -- Deletes a list of edges from a graph
- deleteVertex -- a method for deleting the vertex of a graph
- deleteVertices -- Deletes specified vertices from a digraph or graph
- density -- computes the density of a graph
- depthFirstSearch -- runs a depth first search on the digraph or digraph and returns the discovery time and finishing time for each vertex in the digraph
- descendants -- returns the descendants of a digraph
`descendents`(missing documentation)`DFS`(missing documentation)- diameter -- Computes the diameter of a graph
- digraph -- Constructs a digraph
- digraphTranspose -- returns the transpose of a Digraph
- directProduct -- Computes the direct product of two graphs
`discoveryTime`(missing documentation)- disjointUnion -- Returns the disjoint union of a list of graphs.
- displayGraph -- displays a digraph or graph using Graphviz
- distance -- Computes the distance between two vertexSet in a graph
- distanceMatrix -- Computes the distance matrix of a digraph
- doubleStar -- returns a double star graph
- eccentricity -- Returns the eccentricity of a vertex of a graph
- edgeConnectivity -- computes the edge connectivity of a graph
- edgeCuts -- returns the edge cuts of a graph
- edgeIdeal -- returns the edge ideal of a graph
- edges -- Returns the edges of a digraph or graph
`EntryMode`(missing documentation)- expansion -- returns the expansion of a graph
- findPaths -- finds all the paths in a digraph of a given length starting at a given vertex
`finishingTime`(missing documentation)- floydWarshall -- runs the Floyd-Warshall algorithm on a digraph to determine the minimum distance from one vertex to another in the digraph
`foreFathers`(missing documentation)- forefathers -- returns the forefathers of a digrah
- friendshipGraph -- Returns a friendship Graph
- generalizedPetersenGraph -- Returns a generalized petersen graph
- girth -- A method for computing the girth of a graph
- graph -- Constructs a simple graph
- graph(Digraph) -- Returns the legacy G#graph hash table
- graphComposition -- A method for composing two graphs
- graphLibrary -- constructs a graph of a type specified in the string input
- graphPower -- constructs a graph raised to a power
- hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
- hasOddHole -- checks whether a graph has a odd hole
- incidenceMatrix -- computes the incidence matrix of a graph
- independenceComplex -- constructs the independence complex of a graph
- independenceNumber -- computes the independence number of a graph
- indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
- inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
- isBipartite -- determines whether a graph is bipartite
- isChordal -- checks whether a graph is chordal
- isCM -- determines if a graph is Cohen-Macaulay
- isConnected -- determines whether a graph is connected
- isCyclic -- determines whether a graph is cyclic
- isCyclic(Digraph) -- determines whether a digraph is cyclic
- isEulerian -- determines if a graph or digraph is Eulerian
- isForest -- determines whether a graph is a forest
- isLeaf -- determines whether a vertex is a leaf
- isPerfect -- checks whether a graph is perfect
- isReachable -- checks if a vertex u is reachable from a vertex v
- isRegular -- determines whether a graph is regular
- isRigid -- checks if a graph is rigid
- isSimple -- checks if a graph is simple
- isSink -- determines if a vertex of a digraph is a sink or not
- isSource -- determines if a vertex of a digraph is a source or not
- isStronglyConnected -- checks if a digraph is strongly connected
- isTree -- determines whether a graph is a tree
- isWeaklyConnected -- checks if a digraph is weakly connected
- kneserGraph -- constructs a kneser graph of specified size
`labeledGraph`(missing documentation)- ladderGraph -- Returns a ladder graph
- laplacianMatrix -- Returns the laplacian matrix of a graph
- leaves -- lists the leaves of a tree graph
`lexicographicProduct`(missing documentation)- lineGraph -- Returns the line graph of an undirected graph
- lollipopGraph -- constructs a lollipop graph
- lowestCommonAncestors -- determines the lowest common ancestors between two vertexSet
- minimalDegree -- computes the minimal degree of a graph
- minimalVertexCuts -- finds the minimal vertex cuts of a graph
`mixedGraph`(missing documentation)- monomialGraph -- Returns a monomial graph
- neighbors -- returns the neighbors of a vertex in a graph
`newDigraph`(missing documentation)- nondescendants -- returns the nondescendants of a vertex of a digraph
`nondescendents`(missing documentation)- nonneighbors -- returns the non-neighbors of a vertex in a graph
- numberOfComponents -- computes the number of connected components of a graph
- numberOfTriangles -- counts how many subtriangles are present in a graph
- parents -- returns the parents of a vertex on a digraph
- pathGraph -- A method that makes a path graph
`prismGraph`(missing documentation)- radius -- Returns the radius of a graph
- rattleGraph -- Returns a rattle graph
- reachable -- Returns the vertices reachable in a digraph from a given collection of vertices
- reindexBy -- reindexes the vertices according to the input ordering.
`removeNodes`(missing documentation)- reverseBreadthFirstSearch -- runs a reverse breadth first search on the digraph and returns a list of the vertexSet in the order they were discovered
- showTikZ -- Writes a string of TikZ syntax that can be pasted into a .tex file to display G
`simpleGraph`(missing documentation)`Singletons`(missing documentation)- sinks -- returns the sinks of a digraph
- sources -- returns the sources of a digraph
- spanningForest -- constructs a spanning forest of a graph
- spectrum -- Returns the spectrum of a graph
- starGraph -- Returns a star graph
- strongProduct -- a method for taking the strong product of two graphs
`tensorProduct`(missing documentation)- thresholdGraph -- A method that generates a threshold graph from a binary list
`topologicalSort`(missing documentation)`topSort`(missing documentation)- underlyingGraph -- Returns the underlying graph of a digraph
- vertexConnectivity -- computes the vertex connectivity of a graph
- vertexCoverNumber -- returns the vertex cover number of a graph
- vertexCovers -- returns a list of the minimal vertex covers of a graph
- vertexCuts -- lists all the vertex cuts of a graph
- vertexSet -- Returns the vertices of a graph or digraph
- wheelGraph -- Constructs a wheel graph
- windmillGraph -- Constructs a windmill graph
- writeDotFile -- Writes a graph to a dot file with a specified filename