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Macaulay2 web site
Graphs
::
Graph
Graph
Types of Graph :
Bigraph
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 Cohen-Macaulay
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
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
nonneighbors(Graph,Thing), see
nonneighbors
-- returns the non-neighbors 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
.