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