Graphs : Index

• 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 (missing documentation)
• 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 -- Computes the connected components of a 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
• 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 (missing documentation)
• 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 (missing documentation)
• forefathers -- returns the forefathers of a digrah
• forefathers(Digraph,Thing) -- returns the forefathers of a digrah
• 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 (missing documentation)
• 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