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 "indegree" of a vertex in a digraph

degreeIn(Digraph,Thing)  returns the "indegree" 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 "outdegree" of a vertex in a digraph

degreeOut(Digraph,Thing)  returns the "outdegree" 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  Computes the diameter of a graph

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 FloydWarshall algorithm on a digraph to determine the minimum distance from one vertex to another in the digraph

floydWarshall(Digraph)  runs the FloydWarshall 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

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 CohenMacaulay

isCM(Graph)  determines if a graph is CohenMacaulay

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 nonneighbors of a vertex in a graph

nonneighbors(Graph,Thing)  returns the nonneighbors 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,Graph)  Writes a graph to a dot file with a specified filename