DirectedGraph(S)

graph.spad line 2233 [edit on github]

• S : SetCategory

Category of directed graphs, allows us to model graph theory

* : (%, %) -> DirectedGraph(Product(S, S))

"*"(a,b) returns a tensor product : the tensor product G*H of graphs G and H is a graph such that the vertex set of G*H is the Cartesian product V(G) times V(H); and any two vertices (u, u') and (v, v') are adjacent in G times H if and only if u' is adjacent with v' and u is adjacent with v.

+ : (%, %) -> %

from FiniteGraph(S)

= : (%, %) -> Boolean

from BasicType

addArrow! : (%, Record(name : String, arrType : NonNegativeInteger, fromOb : NonNegativeInteger, toOb : NonNegativeInteger, xOffset : Integer, yOffset : Integer, map : List(NonNegativeInteger))) -> %

from FiniteGraph(S)

addArrow! : (%, String, S, S) -> %

from FiniteGraph(S)

addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger) -> %

from FiniteGraph(S)

addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger, List(NonNegativeInteger)) -> %

from FiniteGraph(S)

addObject! : (%, S) -> %

from FiniteGraph(S)

addObject! : (%, Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger)) -> %

from FiniteGraph(S)

adjacencyMatrix : % -> Matrix(NonNegativeInteger)

from FiniteGraph(S)

arrowName : (%, NonNegativeInteger, NonNegativeInteger) -> String

from FiniteGraph(S)

arrowsFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

cartesian : (%, %) -> DirectedGraph(Product(S, S))

cartesian(a, b) returns a Cartesian product: the vertex set of G o H is the Cartesian product V(G) times V(H) and any two vertices (u, u') and (v, v') are adjacent in G o H if and only if either u = v and u' is adjacent with v' in H, or u' = v' and u is adjacent with v in G.

closedCartesian : (%, %, Mapping(S, S, S)) -> %

closedCartesian(a, b, f) builds Cartesian product of a and b and then maps it back to % using f.

closedTensor : (%, %, Mapping(S, S, S)) -> %

closedTensor(a, b, f) builds tensor product of a and b and then maps it back to % using f.

coerce : FinitePoset(S) -> %

coerce FinitePoset to graph

coerce : List(S) -> %

coerce List to graph

coerce : PermutationGroup(S) -> %

coerce PermutationGroup to graph

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

createWidth : NonNegativeInteger -> NonNegativeInteger

from FiniteGraph(S)

createX : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

createY : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

cycleClosed : (List(S), String) -> %

from FiniteGraph(S)

cycleOpen : (List(S), String) -> %

from FiniteGraph(S)

deepDiagramSvg : (String, %, Boolean) -> Void

from FiniteGraph(S)

diagramHeight : % -> NonNegativeInteger

from FiniteGraph(S)

diagramSvg : (String, %, Boolean) -> Void

from FiniteGraph(S)

diagramWidth : % -> NonNegativeInteger

from FiniteGraph(S)

diagramsSvg : (String, List(%), Boolean) -> Void

from FiniteGraph(S)

directedGraph : FinitePoset(S) -> %

directedGraph(poset) constructs graph from a partially ordered set. This will be a graph with, at most, one arrow between any two nodes.

directedGraph : List(S) -> %

directedGraph(ob) is a constructor for graph with given list of object names and no arrows. Use this version of the constructor if you don't want to create specific x, y coordinates. more objects and arrows can be added later if required.

directedGraph : (List(S), List(List(NonNegativeInteger))) -> %

directedGraph(ob, am) constructs graph with objects ob and adjacency matrix am.

directedGraph : (List(S), List(Record(fromOb : NonNegativeInteger, toOb : NonNegativeInteger))) -> %

directedGraph(obs, ars) constructs graph with objects obs and arrows ars. This constructor just has pure abstract graph information without decoration information.

directedGraph : List(Permutation(S)) -> %

directedGraph(perms) constructs graph from a list of permutations: perms.

directedGraph : List(Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger)) -> %

directedGraph(ob) is a constructor for graph with given objects ob, more objects and arrows can be added later if required.

directedGraph : (List(Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger)), List(Record(name : String, arrType : NonNegativeInteger, fromOb : NonNegativeInteger, toOb : NonNegativeInteger, xOffset : Integer, yOffset : Integer, map : List(NonNegativeInteger)))) -> %

directedGraph(ob, ar) constructs graph with objects ob and arrows ar, more objects and arrows can be added later if required.

distance : (%, NonNegativeInteger, NonNegativeInteger) -> Integer

from FiniteGraph(S)

distanceMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

flatten : DirectedGraph(%) -> %

from FiniteGraph(S)

getArrowIndex : (%, NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

getArrows : % -> List(Record(name : String, arrType : NonNegativeInteger, fromOb : NonNegativeInteger, toOb : NonNegativeInteger, xOffset : Integer, yOffset : Integer, map : List(NonNegativeInteger)))

from FiniteGraph(S)

getVertexIndex : (%, S) -> NonNegativeInteger

from FiniteGraph(S)

getVertices : % -> List(Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger))

from FiniteGraph(S)

inDegree : (%, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

incidenceMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

initial : () -> %

from FiniteGraph(S)

isAcyclic? : % -> Boolean

from FiniteGraph(S)

isDirectSuccessor? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

isDirected? : () -> Boolean

from FiniteGraph(S)

isFixPoint? : (%, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

isFunctional? : % -> Boolean

from FiniteGraph(S)

isGreaterThan? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

kgraph : (List(S), String) -> %

from FiniteGraph(S)

laplacianMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

latex : % -> String

from SetCategory

loopsArrows : % -> List(Loop)

from FiniteGraph(S)

loopsAtNode : (%, NonNegativeInteger) -> List(Loop)

from FiniteGraph(S)

loopsNodes : % -> List(Loop)

from FiniteGraph(S)

looseEquals : (%, %) -> Boolean

from FiniteGraph(S)

map : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %

from FiniteGraph(S)

mapContra : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %

from FiniteGraph(S)

max : % -> NonNegativeInteger

from FiniteGraph(S)

max : (%, List(NonNegativeInteger)) -> NonNegativeInteger

from FiniteGraph(S)

merge : (%, %) -> %

from FiniteGraph(S)

min : % -> NonNegativeInteger

from FiniteGraph(S)

min : (%, List(NonNegativeInteger)) -> NonNegativeInteger

from FiniteGraph(S)

nodeFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

outDegree : (%, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

routeArrows : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

routeNodes : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

spanningForestArrow : % -> List(Tree(Integer))

from FiniteGraph(S)

spanningForestNode : % -> List(Tree(Integer))

from FiniteGraph(S)

spanningTreeArrow : (%, NonNegativeInteger) -> Tree(Integer)

from FiniteGraph(S)

spanningTreeNode : (%, NonNegativeInteger) -> Tree(Integer)

from FiniteGraph(S)

subdiagramSvg : (Scene(SCartesian(2)), %, Boolean, Boolean) -> Void

from FiniteGraph(S)

terminal : S -> %

from FiniteGraph(S)

unit : (List(S), String) -> %

from FiniteGraph(S)

~ : % -> %

The complement or inverse of a graph is a graph on the same vertices such that there is an arrow if and only if there is not an arrow in its compliment. That is, it is the compliment of the arrows but is not the set complement. for more information see: http://en.wikipedia.org/wiki/Complement_graph

~= : (%, %) -> Boolean

from BasicType

FiniteGraph(S)

SetCategory

CoercibleTo(OutputForm)

BasicType