Below is a table of GRAPE commands with the Digraphs counterparts. The sections in this chapter correspond to the chapters in the GRAPE manual.
| GRAPE command | Digraphs command | Comments |
Graph |
Digraph (3.1-7) |
Used with the arguments of Graph in GRAPE , Digraph (3.1-7) will return an equivalent digraph. |
EdgeOrbitsGraph |
EdgeOrbitsDigraph (3.1-10) |
The operation EdgeOrbitsDigraph (3.1-10) behaves the same as EdgeOrbitsDigraph in GRAPE . |
NullGraph |
NullDigraph (3.5-16) or EmptyDigraph (3.5-16) |
Note that, unlike in GRAPE , the arguments of NullDigraph (3.5-16) and EmptyDigraph (3.5-16) are just non-negative integers. Since digraphs in Digraphs are immutable, there is no reason (although it is possible) to create a null digraph and then add edges, as you might be used to doing in GRAPE . |
CompleteGraph |
CompleteDigraph (3.5-11) |
Note that, unlike in GRAPE , the argument to CompleteDigraph (3.5-11) is simply a non-negative integer indicating the number of vertices. By default a complete digraph in Digraphs does not have any loops. If you want a complete digraph with loops at every vertex, then use DigraphAddAllLoops (3.3-45). |
JohnsonGraph |
JohnsonDigraph (3.5-23) |
The GRAPE function JohnsonGraph is equivalent to JohnsonDigraph (3.5-23). |
CayleyGraph |
CayleyDigraph (3.1-12) |
The operation CayleyDigraph (3.1-12) behaves the same as CayleyGraph in GRAPE . |
AddEdgeOrbit |
DigraphAddEdgeOrbit (3.3-18) |
Note that, unlike in GRAPE , digraphs in Digraphs are immutable, and this operation returns a new digraph, i.e. it does not modify the digraph given as an argument. |
RemoveEdgeOrbit |
DigraphRemoveEdgeOrbit (3.3-23) |
Note that, unlike in GRAPE , digraphs in Digraphs are immutable, and this operation returns a new digraph, i.e. it does not modify the digraph given as an argument. |
AssignVertexNames |
SetDigraphVertexLabels (5.1-12) and SetDigraphVertexLabel (5.1-11) |
Use SetDigraphVertexLabel (5.1-11) to set an individual vertex label and SetDigraphVertexLabels (5.1-12) to set all of the vertex labels. |
| GRAPE command | Digraphs command | Comments |
IsGraph |
IsDigraph (3.1-1) |
IsDigraph (3.1-1) is a category and not a function like IsGraph. |
OrderGraph |
DigraphNrVertices (5.1-2) |
The operation DigraphNrVertices (5.1-2) behaves the same as OrderGraph in GRAPE . |
IsVertex(graph, v) |
v in DigraphVertices(digraph) |
The attribute DigraphVertices (5.1-1) can be used to return the list of vertices of a digraph, or if v is known to be a positive integer, then you can simply do v <= DigraphNrVertices(digraph) |
VertexName |
DigraphVertexLabel (5.1-11) |
Unlike VertexName in GRAPE , the return value of DigraphVertexLabel (5.1-11) is mutable. |
VertexNames |
DigraphVertexLabels (5.1-12) |
Unlike VertexNames in GRAPE , the return value of DigraphVertexLabels (5.1-12) is mutable. |
Vertices |
DigraphVertices (5.1-1) |
The vertices of a digraph in Digraphs is always the range [1 .. n] where n is the number of vertices of the digraph. The operation DigraphVertices (5.1-1) behaves the same as Vertices in GRAPE . |
VertexDegree |
OutDegreeOfVertex (5.2-10) (see also: InDegreeOfVertex (5.2-12)) |
The operation OutDegreeOfVertex (5.2-10) behaves the same as VertexDegree in GRAPE . |
VertexDegrees |
OutDegreeSet (5.2-8) (see also: OutDegreeSequence (5.2-8), OutDegrees (5.2-8), InDegrees (5.2-9), InDegreeSequence (5.2-9), InDegreeSet (5.2-9)) |
The operation OutDegreeSet (5.2-8) behaves the same as VertexDegrees in GRAPE . |
IsLoopy |
DigraphHasLoops (6.2-1) |
The operation DigraphHasLoops (6.2-1) behaves the same as IsLoopy in GRAPE . |
IsSimpleGraph |
IsSymmetricDigraph (6.2-14) and not DigraphHasLoops (6.2-1) |
The GRAPE function IsSimpleGraph is equivalent to IsSymmetricDigraph (6.2-14) and not DigraphHasLoops (6.2-1). |
Adjacency |
OutNeighboursOfVertex (5.2-11) (see also InNeighboursOfVertex (5.2-13)) |
The operation OutNeighboursOfVertex (5.2-11) behaves the same as Adjacency in GRAPE . |
IsEdge |
IsDigraphEdge (5.1-17) |
The arguments of IsDigraphEdge (5.1-17) can be a digraph and an edge, or a digraph and two vertices. In the first form the operation IsDigraphEdge (5.1-17) behaves the same as IsEdge in GRAPE . |
DirectedEdges |
DigraphEdges (5.1-3) |
The attribute DigraphEdges (5.1-3) behaves the same as DirectedEdges in GRAPE . |
UndirectedEdges |
None | There is no analogous function in Digraphs, and no plans to include one. |
Distance |
DigraphShortestDistance (5.4-2) |
The operation DigraphShortestDistance (5.4-2) behaves the same as Distance in GRAPE . |
Diameter |
DigraphDiameter (5.4-1) |
The attribute DigraphDiameter (5.4-1) behaves the same as Diameter in GRAPE . |
Girth |
DigraphUndirectedGirth (5.4-8) |
The attribute DigraphUndirectedGirth (5.4-8) behaves the same as Girth in GRAPE except that in the case that the argument is a forest, infinity is returned by Digraphs whereas -1 is returned by GRAPE . |
IsConnectedGraph |
IsStronglyConnectedDigraph (6.6-6) |
The attribute IsStronglyConnectedDigraph (6.6-6) behaves the same as IsConnectedGraph in GRAPE . |
IsBipartite |
IsBipartiteDigraph (6.2-3) and IsSymmetricDigraph (6.2-14) |
The GRAPE function IsBipartite is equivalent to IsBipartiteDigraph (6.2-3) and IsSymmetricDigraph (6.2-14). |
IsNullGraph |
IsNullDigraph (6.2-7) or IsEmptyDigraph (6.2-7) |
The GRAPE function IsNullGraph is equivalent to IsEmptyDigraph (6.2-7) and its synonym IsNullDigraph (6.2-7). |
IsCompleteGraph |
IsCompleteDigraph (6.2-5) |
The GRAPE function IsCompleteGraph is roughly equivalent to IsCompleteDigraph (6.2-5) except that in Digraphs a complete digraph has no loops. |
| GRAPE command | Digraphs command | Comments |
IsRegularGraph |
IsOutRegularDigraph (6.5-2) (see also IsInRegularDigraph (6.5-1) and IsRegularDigraph (6.5-3)) |
The GRAPE function IsRegularGraph is equivalent to IsOutRegularDigraph (6.5-2). |
LocalParameters |
None | The GRAPE function LocalParameters has no equivalent function in Digraphs, although this might change in the future. |
GlobalParameters |
None | The GRAPE function GlobalParameters has no equivalent function in Digraphs, although this might change in the future. |
IsDistanceRegular |
IsDistanceRegularDigraph (6.5-4) |
The GRAPE function IsDistanceRegular is equivalent to IsDistanceRegularDigraph (6.5-4). |
CollapsedAdjacencyMat |
None | The GRAPE function CollapsedAdjacencyMat has no equivalent function in Digraphs, although this might change in the future. |
OrbitalGraphColadjMats |
None | The GRAPE function OrbitalGraphColadjMats has no equivalent function in Digraphs, although this might change in the future. |
VertexTransitiveDRGs |
None | The GRAPE function VertexTransitiveDRGs has no equivalent function in Digraphs, although this might change in the future. |
| GRAPE command | Digraphs command | Comments |
ConnectedComponent |
DigraphConnectedComponent (5.4-10) |
When applied to a simple di/graph and a vertex, ConnectedComponent in GRAPE is equivalent to DigraphConnectedComponent (5.4-10). DigraphConnectedComponent (5.4-10) can also be applied to non-simple graphs (in the language of GRAPE ). |
ConnectedComponents |
DigraphConnectedComponents (5.4-9) |
When applied to a simple di/graph, ConnectedComponents in GRAPE is equivalent to DigraphConnectedComponents (5.4-9). DigraphConnectedComponents (5.4-9) can also be applied to non-simple graphs (in the language of GRAPE ). |
Bicomponents |
DigraphBicomponents (5.4-13) |
When applied to a simple bipartite di/graph, Bicomponents in GRAPE is equivalent to DigraphBicomponents (5.4-13). The definition of IsBipartiteDigraph (6.2-3) does not require its argument to be simple (in the language of GRAPE ), i.e. the bipartite graphs in GRAPE are a proper subset of the bipartite digraphs in Digraphs. |
DistanceSet |
DigraphDistanceSet (5.4-5) |
DistanceSet in GRAPE is equivalent to DigraphDistanceSet (5.4-5) in Digraphs. |
Layers |
DigraphLayers (5.4-34) |
Layers in GRAPE is equivalent to DigraphLayers (5.4-34) in Digraphs. |
IndependentSet |
DigraphIndependentSet (8.2-2) |
IndependentSet in GRAPE is equivalent to DigraphIndependentSet (8.2-2) in Digraphs. |
| GRAPE command | Digraphs command | Comments |
InducedSubgraph |
InducedSubdigraph (3.3-3) |
InducedSubdigraph (3.3-3) in Digraphs does not allow a third argument G specifying a group of automorphisms on the resultant graph. This may be included in a future release. |
DistanceSetInduced |
None | There is no analogous function in Digraphs, and no plans to include one. |
DistanceGraph |
DistanceDigraph (3.3-46) |
DistanceGraph in GRAPE is equivalent to DistanceDigraph (3.3-46) in Digraphs. |
ComplementGraph |
DigraphDual (3.3-11) |
DigraphDual (3.3-11) in Digraphs is equivalent to ComplementGraph in GRAPE with the optional argument comploops set to true (loops/nonloops are complemented). |
PointGraph |
None | There is no analogous function in Digraphs, and no plans to include one. |
EdgeGraph |
EdgeUndirectedDigraph (3.3-42) |
EdgeGraph in GRAPE is equivalent to EdgeUndirectedDigraph (3.3-42) in Digraphs. |
SwitchedGraph |
None | There is no analogous function in Digraphs, and no plans to include one. |
UnderlyingGraph |
DigraphSymmetricClosure (3.3-12) |
UnderlyingGraph in GRAPE is equivalent to DigraphSymmetricClosure (3.3-12) in Digraphs. |
QuotientGraph |
QuotientDigraph (3.3-9) |
QuotientDigraph (3.3-9) in Digraphs takes a partition p of the vertices of the digraph, rather than a set of generating pairs. Hence, the equivalence might not be group-invariant. Also note that in Digraphs multiple edges may be created, whereas in GRAPE they are effectively combined into a single edge. |
BipartiteDouble |
BipartiteDoubleDigraph (3.3-44) |
BipartiteDouble in GRAPE is equivalent to BipartiteDoubleDigraph (3.3-44) in Digraphs. |
GeodesicsGraph |
None | There is no analogous function in Digraphs, and no plans to include one. |
CollapsedIndependentOrbitsGraph |
None | There is no analogous function in Digraphs, although this feature might be implemented in the future. |
CollapsedCompleteOrbitsGraph |
None | There is no analogous function in Digraphs, although this feature might be implemented in the future. |
NewGroupGraph |
None | There is no analogous function in Digraphs. However, the same results would be possible by calling DigraphCopy (3.3-1) on the digraph to produce a copy gr, and then applying SetDigraphGroup(gr, G). |
| GRAPE command | Digraphs command | Comments |
VertexColouring |
DigraphGreedyColouring (7.3-16) |
VertexColouring in GRAPE is equivalent to DigraphGreedyColouring (7.3-16) in Digraphs, except it returns a transformation rather than a list of vertex colors. |
CompleteSubgraphs |
DigraphCliques (8.1-4) |
The functionality of CompleteSubgraphs in GRAPE is provided by DigraphCliques (8.1-4) and DigraphMaximalCliques (8.1-4) in Digraphs. |
CompleteSubgraphsOfGivenSize |
DigraphCliques (8.1-4) |
Much of the functionality of CompleteSubgraphsOfGivenSize in GRAPE is provided by DigraphCliques (8.1-4) and DigraphMaximalCliques (8.1-4) in Digraphs, except that the functionality relating to vertex weights and partial colourings is not implemented. |
| GRAPE command | Digraphs command | Comments |
AutGroupGraph |
AutomorphismGroup (7.2-2) |
AutGroupGraph in GRAPE is equivalent to AutomorphismGroup (7.2-2) in Digraphs. |
GraphIsomorphism |
IsomorphismDigraphs (7.2-17) |
GraphIsomorphism in GRAPE is equivalent to IsomorphismDigraphs (7.2-17) in Digraphs. Note however that GraphIsomorphism's optional argument firstunbindcanon is not applicable, since the canonical labellings of a digraph are not portable between sessions. |
IsIsomorphicGraph |
IsIsomorphicDigraph (7.2-15) |
IsIsomorphicGraph in GRAPE is equivalent to IsIsomorphicDigraph (7.2-15) in Digraphs. Note however that IsIsomorphicGraph's optional argument firstunbindcanon is not applicable, since the canonical labellings of a digraph are not portable between sessions. |
GraphIsomorphismClassRepresentatives |
None | There is no analogous function in Digraphs, although this feature might be implemented in the future. |
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