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Macaulay2 website
Graphs
::
Graph
Graph
Functions and methods returning an object of class Graph :
"addEdge(Digraph,Set)"
 see
addEdge
 A method for adding edges to a graph
addEdges'(Graph,List)
(missing documentation)
"addVertices(Digraph,List)"
 see
addVertex
 A method for adding a set of vertices to a graph
addVertices(Graph,List)
(missing documentation)
"barbellGraph(ZZ)"
 see
barbellGraph
 Returns the barbell graph
"barycenter(Graph)"
 see
barycenter
 Returns the barycenter of a grah
"cartesianProduct(Graph,Graph)"
 see
cartesianProduct
 Computes the cartesian product of two graphs
"circularLadder(ZZ)"
 see
circularLadder
 Returns a circular ladder graph
"cocktailParty(ZZ)"
 see
cocktailParty
 Returns a cocktail party graph
"complementGraph(Graph)"
 see
complementGraph
 Returns the complement of a graph
"completeGraph(ZZ)"
 see
completeGraph
 Constructs a complete graph
"completeMultipartiteGraph(List)"
 see
completeMultipartiteGraph
 constructs a complete multipartite graph
"crownGraph(ZZ)"
 see
crownGraph
 Returns a crown graph
"cycleGraph(ZZ)"
 see
cycleGraph
 Constructs a cycle graph
"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
"directProduct(Graph,Graph)"
 see
directProduct
 Computes the direct product of two graphs
"disjointUnion(List)"
 see
disjointUnion
 Returns the disjoint union of a list of graphs.
"doubleStar(ZZ,ZZ)"
 see
doubleStar
 returns a double star graph
"friendshipGraph(ZZ)"
 see
friendshipGraph
 Returns a friendship Graph
"generalizedPetersenGraph(ZZ,ZZ)"
 see
generalizedPetersenGraph
 Returns a generalized petersen graph
"graph(HashTable)"
 see
graph
 Constructs a simple graph
"graph(List)"
 see
graph
 Constructs a simple graph
"graph(List,List)"
 see
graph
 Constructs a simple graph
"graph(List,Matrix)"
 see
graph
 Constructs a simple graph
"graph(Matrix)"
 see
graph
 Constructs a simple graph
"graphComposition(Graph,Graph)"
 see
graphComposition
 A method for composing two graphs
"graphLibrary(String)"
 see
graphLibrary
 constructs a graph of a type specified in the string input
"graphPower(Graph,ZZ)"
 see
graphPower
 constructs a graph raised to a power
"indexLabelGraph(Graph)"
 see
indexLabelGraph
 Relabels the vertices of a graph or digraph according to their indices, indexed from 0.
"inducedSubgraph(Graph,List)"
 see
inducedSubgraph
 A method for finding the induced subgraph of any Graph or Digraph
"kneserGraph(ZZ,ZZ)"
 see
kneserGraph
 constructs a kneser graph of specified size
"ladderGraph(ZZ)"
 see
ladderGraph
 Returns a ladder graph
"lineGraph(Graph)"
 see
lineGraph
 Returns the line graph of an undirected graph
"lollipopGraph(ZZ,ZZ)"
 see
lollipopGraph
 constructs a lollipop graph
"monomialGraph(MonomialIdeal,ZZ)"
 see
monomialGraph
 Returns a monomial graph
"pathGraph(ZZ)"
 see
pathGraph
 A method that makes a path graph
"rattleGraph(ZZ,ZZ)"
 see
rattleGraph
 Returns a rattle graph
"reindexBy(Graph,String)"
 see
reindexBy
 reindexes the vertices according to the input ordering.
"spanningForest(Graph)"
 see
spanningForest
 constructs a spanning forest of a graph
"starGraph(ZZ)"
 see
starGraph
 Returns a star graph
"strongProduct(Graph,Graph)"
 see
strongProduct
 a method for taking the strong product of two graphs
"thresholdGraph(List)"
 see
thresholdGraph
 A method that generates a threshold graph from a binary list
"underlyingGraph(Digraph)"
 see
underlyingGraph
 Returns the underlying graph of a digraph
"vertexMultiplication(Graph,Thing,Thing)"
 see
vertexMultiplication
"wheelGraph(ZZ)"
 see
wheelGraph
 Constructs a wheel graph
"windmillGraph(ZZ,ZZ)"
 see
windmillGraph
 Constructs a windmill graph
Methods that use an object of class Graph :
"bipartiteColoring(Graph)"
 see
bipartiteColoring
 Returns a coloring of a bipartite graph
"center(Graph)"
 see
center
 Returns the center of a graph
"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)
"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(Graph,Thing)
(missing documentation)
"degreeCentrality(Graph,Thing)"
 see
degreeCentrality
 Returns the degreeCentrality of a vertex of a graph
"density(Graph)"
 see
density
 computes the density of a graph
"diameter(Graph)"
 see
diameter
 Computes the diameter of a graph
"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(Graph)"
 see
edges
 Returns the edges of a digraph or graph
"expansion(Graph)"
 see
expansion
 returns the expansion of a graph
"girth(Graph)"
 see
girth
 A method for computing the girth of a graph
"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
"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 CohenMacaulay
"isConnected(Graph)"
 see
isConnected
 determines whether a graph is connected
"isCyclic(Graph)"
 see
isCyclic
 determines whether a graph is cyclic
"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
"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
"isTree(Graph)"
 see
isTree
 determines whether a graph is a tree
"laplacianMatrix(Graph)"
 see
laplacianMatrix
 Returns the laplacian matrix of a graph
"leaves(Graph)"
 see
leaves
 lists the leaves of a tree graph
"minimalDegree(Graph)"
 see
minimalDegree
 computes the minimal degree of a graph
"minimalVertexCuts(Graph)"
 see
minimalVertexCuts
 finds the minimal vertex cuts of a graph
"neighbors(Graph,Thing)"
 see
neighbors
 returns the neighbors of a vertex in a graph
"nonneighbors(Graph,Thing)"
 see
nonneighbors
 returns the nonneighbors of a vertex in a graph
"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
"radius(Graph)"
 see
radius
 Returns the radius of a graph
"spectrum(Graph)"
 see
spectrum
 Returns the spectrum of a graph
"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
"writeDotFile(String,Graph)"
 see
writeDotFile
 Writes a graph to a dot file with a specified filename
For the programmer
The object
Graph
is
a
type
, with ancestor classes
Digraph
<
HashTable
<
Thing
.