DirectedGraph S¶

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

~=: (%, %) -> Boolean

from BasicType

~: % -> %

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

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

from FiniteGraph S

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

from FiniteGraph S

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

from FiniteGraph S

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

from FiniteGraph S

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

from FiniteGraph S

from FiniteGraph S

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

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

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

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

coerce: % -> OutputForm
coerce: FinitePoset S -> %

coerce FinitePoset to graph

coerce: List S -> %

coerce List to graph

coerce: PermutationGroup S -> %

coerce PermutationGroup to graph

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

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

from FiniteGraph S

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

from FiniteGraph S

diagramWidth: % -> NonNegativeInteger

from FiniteGraph S

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.

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: 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 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 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.

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

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

incidenceMatrix: % -> Matrix Integer

from FiniteGraph S

inDegree: (%, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph S

initial: () -> %

from FiniteGraph S

isAcyclic?: % -> Boolean

from FiniteGraph S

isDirected?: () -> Boolean

from FiniteGraph S

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

BasicType

SetCategory