- Jack Burkart <jburkar1@nd.edu>
- Caroline Jansen <cjansen@nd.edu>
- Amelia Taylor <originalbrickhouse@gmail.com>
- Augustine O'Keefe <aokeefe@tulane.edu>
- Contributers of note: Alex Diaz, Luis Garcia, Shaowei Lin, Sonja Mapes, Mike Stillman, Doug Torrance

- Functions and commands
- addEdge -- A method for adding edges to a graph
- addEdges', see addEdge -- A method for adding edges to a graph
- addVertex -- A method for adding a set of vertices to a graph
- addVertices, see 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
- 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
- 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
- expansion -- returns the expansion of a graph
- findPaths -- finds all the paths in a digraph of a given length starting at a given vertex
- 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
- 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
- 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
- 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
- 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
- vertexMultiplication
- 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

- Methods
- addEdge(Digraph,Set), see addEdge -- A method for adding edges to a graph
- addEdges'(Digraph,List), see addEdge -- A method for adding edges to a graph
`addEdges'(Graph,List)`(missing documentation)- addVertex(Digraph,Thing), see addVertex -- A method for adding a set of vertices to a graph
- addVertices(Digraph,List), see addVertex -- A method for adding a set of vertices to a graph
`addVertices(Graph,List)`(missing documentation)- adjacencyMatrix(Digraph), see adjacencyMatrix -- Returns the adjacency matrix of a Graph or Digraph
- barycenter(Graph), see barycenter -- Returns the barycenter of a grah
`bigraph(MixedGraph)`(missing documentation)- bipartiteColoring(Graph), see bipartiteColoring -- Returns a coloring of a bipartite graph
- breadthFirstSearch(Digraph,Thing), see 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(Graph,Graph), see cartesianProduct -- Computes the cartesian product of two graphs
- center(Graph), see center -- Returns the center of a graph
- children(Digraph,Thing), see children -- returns the children of a vertex of a digraph
`children(MixedGraph,Thing)`(missing documentation)- 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)`collateVertices(MixedGraph)`(missing documentation)- complementGraph(Graph), see complementGraph -- Returns the complement of a graph
- 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(Digraph,Thing) -- returns the degree of a vertex in a digraph
`degree(Graph,Thing)`(missing documentation)- degreeCentrality(Graph,Thing), see degreeCentrality -- Returns the degreeCentrality of a vertex of a graph
- degreeIn(Digraph,Thing), see degreeIn -- returns the "in-degree" of a vertex in a digraph
- degreeMatrix(Digraph), see degreeMatrix -- Returns the degree matrix of a graph
- degreeOut(Digraph,Thing), see degreeOut -- returns the "out-degree" of a vertex in a digraph
- 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
`deleteVertex(Digraph,Thing)`(missing documentation)- deleteVertices(Digraph,List), see deleteVertices -- Deletes specified vertices from a digraph or graph
- density(Graph), see density -- computes the density of a graph
- depthFirstSearch(Digraph), see 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(Digraph,Thing), see descendants -- returns the descendants of a digraph
`descendants(MixedGraph,Thing)`(missing documentation)- diameter(Graph), see diameter -- Computes the diameter of a graph
`Digraph _ List`(missing documentation)`Digraph _ ZZ`(missing documentation)`Digraph _*`(missing documentation)`digraph(MixedGraph)`(missing documentation)- digraphTranspose(Digraph), see digraphTranspose -- returns the transpose of a Digraph
- directProduct(Graph,Graph), see directProduct -- Computes the direct product of two graphs
- displayGraph(Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- displayGraph(String,Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- displayGraph(String,String,Digraph), see displayGraph -- displays a digraph or graph using Graphviz
- distance(Digraph,Thing,Thing), see distance -- Computes the distance between two vertexSet in a graph
`distance(Digraph,Thing)`(missing documentation)- distanceMatrix(Digraph), see distanceMatrix -- Computes the distance matrix of a digraph
- 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(Digraph), see edges -- Returns the edges of a digraph or graph
- edges(Graph), see edges -- Returns the edges of a digraph or graph
- expansion(Graph), see expansion -- returns the expansion of a graph
- findPaths(Digraph,Thing,ZZ), see findPaths -- finds all the paths in a digraph of a given length starting at a given vertex
- floydWarshall(Digraph), see floydWarshall -- runs the Floyd-Warshall algorithm on a digraph to determine the minimum distance from one vertex to another in the digraph
- forefathers(Digraph,Thing), see forefathers -- returns the forefathers of a digrah
`forefathers(MixedGraph,Thing)`(missing documentation)- girth(Graph), see girth -- A method for computing the girth of a graph
- graph(Digraph) -- Returns the legacy G#graph hash table
`graph(LabeledGraph)`(missing documentation)`graph(MixedGraph)`(missing documentation)- graphComposition(Graph,Graph), see graphComposition -- A method for composing two graphs
- graphPower(Graph,ZZ), see graphPower -- constructs a graph raised to a power
- hasEulerianTrail(Digraph), see hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail
- 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
- indexLabelGraph(Digraph), see indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
- indexLabelGraph(Graph), see indexLabelGraph -- Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
- inducedSubgraph(Digraph,List), see inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
- inducedSubgraph(Graph,List), see inducedSubgraph -- A method for finding the induced subgraph of any Graph or Digraph
- 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
- isCyclic(Digraph) -- determines whether a digraph is cyclic
- isEulerian(Digraph), see isEulerian -- determines if a graph or digraph is Eulerian
- 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
- isReachable(Digraph,Thing,Thing), see isReachable -- checks if a vertex u is reachable from a vertex v
- 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
- isSink(Digraph,Thing), see isSink -- determines if a vertex of a digraph is a sink or not
- isSource(Digraph,Thing), see isSource -- determines if a vertex of a digraph is a source or not
- isStronglyConnected(Digraph), see isStronglyConnected -- checks if a digraph is strongly connected
- isTree(Graph), see isTree -- determines whether a graph is a tree
- isWeaklyConnected(Digraph), see isWeaklyConnected -- checks if a digraph is weakly connected
`labeledGraph(Digraph,List)`(missing documentation)- laplacianMatrix(Graph), see laplacianMatrix -- Returns the laplacian matrix of a graph
- leaves(Graph), see leaves -- lists the leaves of a tree graph
- lineGraph(Graph), see lineGraph -- Returns the line graph of an undirected graph
- lowestCommonAncestors(Digraph,Thing,Thing), see lowestCommonAncestors -- determines the lowest common ancestors between two vertexSet
- minimalDegree(Graph), see minimalDegree -- computes the minimal degree of a graph
- minimalVertexCuts(Graph), see minimalVertexCuts -- finds the minimal vertex cuts of a graph
`mixedGraph(Digraph)`(missing documentation)`mixedGraph(Digraph,Bigraph)`(missing documentation)`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
`neighbors(MixedGraph,Thing)`(missing documentation)`net(Digraph)`(missing documentation)`net(LabeledGraph)`(missing documentation)`net(MixedGraph)`(missing documentation)- nondescendants(Digraph,Thing), see nondescendants -- returns the nondescendants of a vertex of a digraph
`nondescendants(MixedGraph,Thing)`(missing documentation)- nonneighbors(Graph,Thing), see nonneighbors -- returns the non-neighbors of a vertex in a graph
`nonneighbors(MixedGraph,Thing)`(missing documentation)- 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
- parents(Digraph,Thing), see parents -- returns the parents of a vertex on a digraph
`parents(MixedGraph,Thing)`(missing documentation)- radius(Graph), see radius -- Returns the radius of a graph
- reachable(Digraph,List), see reachable -- Returns the vertices reachable in a digraph from a given collection of vertices
- reachable(Digraph,Set), see reachable -- Returns the vertices reachable in a digraph from a given collection of vertices
- reindexBy(Digraph,String), see reindexBy -- reindexes the vertices according to the input ordering.
- reindexBy(Graph,String), see reindexBy -- reindexes the vertices according to the input ordering.
- reverseBreadthFirstSearch(Digraph,Thing), see reverseBreadthFirstSearch -- runs a reverse breadth first search on the digraph and returns a list of the vertexSet in the order they were discovered
- showTikZ(Digraph), see showTikZ -- Writes a string of TikZ syntax that can be pasted into a .tex file to display G
- sinks(Digraph), see sinks -- returns the sinks of a digraph
- sources(Digraph), see sources -- returns the sources of a digraph
- spanningForest(Graph), see spanningForest -- constructs a spanning forest of a graph
- spectrum(Graph), see spectrum -- Returns the spectrum of a graph
- strongProduct(Graph,Graph), see strongProduct -- a method for taking the strong product of two graphs
`topologicalSort(Digraph)`(missing documentation)`topologicalSort(Digraph,String)`(missing documentation)`topSort(Digraph)`(missing documentation)`toString(Digraph)`(missing documentation)`toString(LabeledGraph)`(missing documentation)`toString(MixedGraph)`(missing documentation)- underlyingGraph(Digraph), see underlyingGraph -- Returns the underlying graph of a digraph
- 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
- vertexMultiplication(Graph,Thing,Thing), see vertexMultiplication
- vertexSet(Digraph), see vertexSet -- Returns the vertices of a graph or digraph
- vertices(Digraph), see vertexSet -- Returns the vertices of a graph or digraph
`vertices(MixedGraph)`(missing documentation)- writeDotFile(String,Graph), see writeDotFile -- Writes a graph to a dot file with a specified filename

- Symbols
`discoveryTime`(missing documentation)`EntryMode`(missing documentation)`finishingTime`(missing documentation)`newDigraph`(missing documentation)`simpleGraph`(missing documentation)`Singletons`(missing documentation)