  
  
                                   [1X Digraphs [101X
  
  
                  [1X Graphs, digraphs, and multidigraphs in [5XGAP[105X [101X
  
  
                                     1.9.0
  
  
                                6 September 2024
  
  
                                  Jan De Beule
  
                                 Julius Jonusas
  
                                 James Mitchell
  
                                 Wilf A. Wilson
  
                                 Michael Young
  
                        Marina Anagnostopoulou-Merkouri
  
                                   Finn Buck
  
                                 Stuart Burrell
  
                                Graham Campbell
  
                                Raiyan Chowdhury
  
                                 Reinis Cirpons
  
                                 Ashley Clayton
  
                                Tom Conti-Leslie
  
                                 Joseph Edwards
  
                                  Luna Elliott
  
                                 Isuru Fernando
  
                                 Ewan Gilligan
  
                               Sebastian Gutsche
  
                                Samantha Harper
  
                                    Max Horn
  
                             Christopher Jefferson
  
                               Olexandr Konovalov
  
                                 Hyeokjun Kwon
  
                                   Andrea Lee
  
                                 Saffron McIver
  
                                Michael Orlitzky
  
                                 Matthew Pancer
  
                                Markus Pfeiffer
  
                                 Daniel Pointon
  
                                   Lea Racine
  
                              Christopher Russell
  
                                 Artur Schaefer
  
                                 Isabella Scott
  
                                 Kamran Sharma
  
                                   Finn Smith
  
                                   Ben Spiers
  
                                 Maria Tsalakou
  
                                  Meike Weiss
  
                                  Murray Whyte
  
                                Fabian Zickgraf
  
  
  
  Jan De Beule
      Email:    [7Xmailto:jdebeule@cage.ugent.be[107X
      Homepage: [7Xhttp://homepages.vub.ac.be/~jdbeule/[107X
      Address:  [33X[0;14YVrije  Universiteit Brussel, Vakgroep Wiskunde, Pleinlaan 2, B
                - 1050 Brussels, Belgium[133X
  
  
  Julius Jonusas
      Email:    [7Xmailto:j.jonusas@gmail.com[107X
      Homepage: [7Xhttp://julius.jonusas.work[107X
  James Mitchell
      Email:    [7Xmailto:jdm3@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://jdbm.me[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Wilf A. Wilson
      Email:    [7Xmailto:gap@wilf-wilson.net[107X
      Homepage: [7Xhttps://wilf.me[107X
  Michael Young
      Email:    [7Xmailto:mct25@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://mct25.host.cs.st-andrews.ac.uk[107X
      Address:  [33X[0;14YJack  Cole  Building, North Haugh, St Andrews, Fife, KY16 9SX,
                Scotland[133X
  
  
  Marina Anagnostopoulou-Merkouri
      Email:    [7Xmailto:mam49@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Finn Buck
      Email:    [7Xmailto:finneganlbuck@gmail.com[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Stuart Burrell
      Email:    [7Xmailto:stuartburrell1994@gmail.com[107X
      Homepage: [7Xhttps://stuartburrell.github.io[107X
  Reinis Cirpons
      Email:    [7Xmailto:rc234@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Ashley Clayton
      Email:    [7Xmailto:ac323@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Tom Conti-Leslie
      Email:    [7Xmailto:tom.contileslie@gmail.com[107X
      Homepage: [7Xhttps://tomcontileslie.com[107X
  Joseph Edwards
      Email:    [7Xmailto:jde1@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://github.com/Joseph-Edwards[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Luna Elliott
      Email:    [7Xmailto:TODO[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Isuru Fernando
      Email:    [7Xmailto:isuruf@gmail.com[107X
  Ewan Gilligan
      Email:    [7Xmailto:eg207@st-andrews.ac.uk[107X
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@momo.math.rwth-aachen.de[107X
  Samantha Harper
      Email:    [7Xmailto:seh25@st-andrews.ac.uk[107X
  Max Horn
      Email:    [7Xmailto:horn@mathematik.uni-kl.de[107X
      Homepage: [7Xhttps://www.quendi.de/math[107X
      Address:  [33X[0;14YFachbereich        Mathematik,        TU       Kaiserslautern,
                Gottlieb-Daimler-Straße 48, 67663 Kaiserslautern, Germany[133X
  
  
  Christopher Jefferson
      Email:    [7Xmailto:caj21@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://caj.host.cs.st-andrews.ac.uk[107X
      Address:  [33X[0;14YJack  Cole  Building, North Haugh, St Andrews, Fife, KY16 9SX,
                Scotland[133X
  
  
  Olexandr Konovalov
      Email:    [7Xmailto:obk1@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://olexandr-konovalov.github.io/[107X
      Address:  [33X[0;14YJack  Cole  Building, North Haugh, St Andrews, Fife, KY16 9SX,
                Scotland[133X
  
  
  Hyeokjun Kwon
      Email:    [7Xmailto:hk78@st-andrews.ac.uk[107X
  Andrea Lee
      Email:    [7Xmailto:ahwl1@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Saffron McIver
      Email:    [7Xmailto:sm544@st-andrews.ac.uk[107X
  Michael Orlitzky
      Email:    [7Xmailto:michael@orlitzky.com[107X
      Homepage: [7Xhttps://michael.orlitzky.com/[107X
  Matthew Pancer
      Email:    [7Xmailto:mp322@st-andrews.ac.uk[107X
  Markus Pfeiffer
      Email:    [7Xmailto:markus.pfeiffer@morphism.de[107X
      Homepage: [7Xhttps://markusp.morphism.de/[107X
  Daniel Pointon
      Email:    [7Xmailto:dp211@st-andrews.ac.uk[107X
  Lea Racine
      Email:    [7Xmailto:lr217@st-andrews.ac.uk[107X
      Address:  [33X[0;14YJack  Cole  Building, North Haugh, St Andrews, Fife, KY16 9SX,
                Scotland[133X
  
  
  Artur Schaefer
      Email:    [7Xmailto:as305@st-and.ac.uk[107X
  Isabella Scott
      Email:    [7Xmailto:iscott@uchicago.edu[107X
  Kamran Sharma
      Email:    [7Xmailto:kks4@st-andrews.ac.uk[107X
      Address:  [33X[0;14YJack  Cole  Building, North Haugh, St Andrews, Fife, KY16 9SX,
                Scotland[133X
  
  
  Finn Smith
      Email:    [7Xmailto:fls3@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Ben Spiers
      Email:    [7Xmailto:bspiers972@outlook.com[107X
  Maria Tsalakou
      Email:    [7Xmailto:mt200@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://mariatsalakou.github.io/[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Meike Weiss
      Email:    [7Xmailto:weiss@art.rwth-aachen.de[107X
      Homepage: [7Xhttps://bit.ly/4e6pUeP[107X
      Address:  [33X[0;14YChair of Algebra and Representation Theory, Pontdriesch 10-16,
                52062 Aachen[133X
  
  
  Murray Whyte
      Email:    [7Xmailto:mw231@st-andrews.ac.uk[107X
      Address:  [33X[0;14YMathematical  Institute,  North  Haugh, St Andrews, Fife, KY16
                9SS, Scotland[133X
  
  
  Fabian Zickgraf
      Email:    [7Xmailto:f.zickgraf@dashdos.com[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XDigraphs[105X  package  is  a  [5XGAP[105X  package  containing  methods for graphs,
  digraphs, and multidigraphs.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0YJan  De  Beule,  Julius  Jonušas, James D. Mitchell, Wilf A. Wilson, Michael
  Young et al.[133X
  
  [33X[0;0Y[5XDigraphs[105X  is  free  software; you can redistribute it and/or modify it under
  the      terms      of      the      GNU      General     Public     License
  ([7Xhttps://www.fsf.org/licenses/gpl.html[107X)  as  published  by the Free Software
  Foundation;  either  version 3 of the License, or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YWe would like to thank Christopher Jefferson for his help in including [5Xbliss[105X
  in  [5XDigraphs[105X. This package's methods for computing digraph homomorphisms are
  based on work by Max Neunhöffer, and independently Artur Schäfer.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Digraphs)[101X
  
  1 [33X[0;0YThe [5XDigraphs[105X package[133X
    1.1 [33X[0;0YIntroduction[133X
      1.1-1 [33X[0;0YDefinitions[133X
  2 [33X[0;0YInstalling [5XDigraphs[105X[133X
    2.1 [33X[0;0YFor those in a hurry[133X
      2.1-1 [33X[0;0YConfiguration options[133X
    2.2 [33X[0;0YOptional package dependencies[133X
      2.2-1 [33X[0;0YThe Grape package[133X
    2.3 [33X[0;0YCompiling the kernel module[133X
    2.4 [33X[0;0YRebuilding the documentation[133X
      2.4-1 DigraphsMakeDoc
    2.5 [33X[0;0YTesting your installation[133X
      2.5-1 DigraphsTestInstall
      2.5-2 DigraphsTestStandard
      2.5-3 DigraphsTestExtreme
  3 [33X[0;0YCreating digraphs[133X
    3.1 [33X[0;0YCreating digraphs[133X
      3.1-1 IsDigraph
      3.1-2 IsMutableDigraph
      3.1-3 IsImmutableDigraph
      3.1-4 IsCayleyDigraph
      3.1-5 IsDigraphWithAdjacencyFunction
      3.1-6 DigraphByOutNeighboursType
      3.1-7 Digraph
      3.1-8 DigraphByAdjacencyMatrix
      3.1-9 DigraphByEdges
      3.1-10 EdgeOrbitsDigraph
      3.1-11 DigraphByInNeighbours
      3.1-12 CayleyDigraph
      3.1-13 ListNamedDigraphs
    3.2 [33X[0;0YChanging representations[133X
      3.2-1 AsBinaryRelation
      3.2-2 AsDigraph
      3.2-3 Graph
      3.2-4 AsGraph
      3.2-5 AsTransformation
    3.3 [33X[0;0YNew digraphs from old[133X
      3.3-1 DigraphImmutableCopy
      3.3-2 DigraphImmutableCopyIfImmutable
      3.3-3 InducedSubdigraph
      3.3-4 ReducedDigraph
      3.3-5 MaximalSymmetricSubdigraph
      3.3-6 MaximalAntiSymmetricSubdigraph
      3.3-7 UndirectedSpanningForest
      3.3-8 DigraphShortestPathSpanningTree
      3.3-9 QuotientDigraph
      3.3-10 DigraphReverse
      3.3-11 DigraphDual
      3.3-12 DigraphSymmetricClosure
      3.3-13 DigraphTransitiveClosure
      3.3-14 DigraphTransitiveReduction
      3.3-15 DigraphAddVertex
      3.3-16 DigraphAddVertices
      3.3-17 DigraphAddEdge
      3.3-18 DigraphAddEdgeOrbit
      3.3-19 DigraphAddEdges
      3.3-20 DigraphRemoveVertex
      3.3-21 DigraphRemoveVertices
      3.3-22 DigraphRemoveEdge
      3.3-23 DigraphRemoveEdgeOrbit
      3.3-24 DigraphRemoveEdges
      3.3-25 DigraphRemoveLoops
      3.3-26 DigraphRemoveAllMultipleEdges
      3.3-27 DigraphContractEdge
      3.3-28 DigraphReverseEdges
      3.3-29 DigraphDisjointUnion
      3.3-30 DigraphEdgeUnion
      3.3-31 DigraphJoin
      3.3-32 DigraphCartesianProduct
      3.3-33 DigraphDirectProduct
      3.3-34 ConormalProduct
      3.3-35 HomomorphicProduct
      3.3-36 LexicographicProduct
      3.3-37 ModularProduct
      3.3-38 StrongProduct
      3.3-39 DigraphCartesianProductProjections
      3.3-40 DigraphDirectProductProjections
      3.3-41 LineDigraph
      3.3-42 LineUndirectedDigraph
      3.3-43 DoubleDigraph
      3.3-44 BipartiteDoubleDigraph
      3.3-45 DigraphAddAllLoops
      3.3-46 DistanceDigraph
      3.3-47 DigraphClosure
      3.3-48 DigraphMycielskian
    3.4 [33X[0;0YRandom digraphs[133X
      3.4-1 RandomDigraph
      3.4-2 RandomMultiDigraph
      3.4-3 RandomTournament
      3.4-4 RandomLattice
    3.5 [33X[0;0YStandard examples[133X
      3.5-1 AndrasfaiGraph
      3.5-2 BananaTree
      3.5-3 BinaryTree
      3.5-4 BinomialTreeGraph
      3.5-5 BishopsGraph
      3.5-6 BondyGraph
      3.5-7 BookGraph
      3.5-8 StackedBookGraph
      3.5-9 ChainDigraph
      3.5-10 CirculantGraph
      3.5-11 CompleteDigraph
      3.5-12 CompleteBipartiteDigraph
      3.5-13 CompleteMultipartiteDigraph
      3.5-14 CycleDigraph
      3.5-15 CycleGraph
      3.5-16 EmptyDigraph
      3.5-17 GearGraph
      3.5-18 HaarGraph
      3.5-19 HalvedCubeGraph
      3.5-20 HanoiGraph
      3.5-21 HelmGraph
      3.5-22 HypercubeGraph
      3.5-23 JohnsonDigraph
      3.5-24 KellerGraph
      3.5-25 KingsGraph
      3.5-26 KneserGraph
      3.5-27 KnightsGraph
      3.5-28 LindgrenSousselierGraph
      3.5-29 LollipopGraph
      3.5-30 MobiusLadderGraph
      3.5-31 MycielskiGraph
      3.5-32 OddGraph
      3.5-33 PathGraph
      3.5-34 PermutationStarGraph
      3.5-35 PetersenGraph
      3.5-36 GeneralisedPetersenGraph
      3.5-37 PrismGraph
      3.5-38 StackedPrismGraph
      3.5-39 QueensGraph
      3.5-40 RooksGraph
      3.5-41 SquareGridGraph
      3.5-42 TriangularGridGraph
      3.5-43 StarGraph
      3.5-44 TadpoleGraph
      3.5-45 WalshHadamardGraph
      3.5-46 WebGraph
      3.5-47 WheelGraph
      3.5-48 WindmillGraph
  4 [33X[0;0YOperators[133X
    4.1 [33X[0;0YOperators for digraphs[133X
      4.1-1 IsSubdigraph
      4.1-2 IsUndirectedSpanningTree
  5 [33X[0;0YAttributes and operations[133X
    5.1 [33X[0;0YVertices and edges[133X
      5.1-1 DigraphVertices
      5.1-2 DigraphNrVertices
      5.1-3 DigraphEdges
      5.1-4 DigraphNrEdges
      5.1-5 DigraphNrAdjacencies
      5.1-6 DigraphNrAdjacenciesWithoutLoops
      5.1-7 DigraphNrLoops
      5.1-8 DigraphSinks
      5.1-9 DigraphSources
      5.1-10 DigraphTopologicalSort
      5.1-11 DigraphVertexLabel
      5.1-12 DigraphVertexLabels
      5.1-13 DigraphEdgeLabel
      5.1-14 DigraphEdgeLabels
      5.1-15 DigraphInEdges
      5.1-16 DigraphOutEdges
      5.1-17 IsDigraphEdge
      5.1-18 IsMatching
      5.1-19 DigraphMaximalMatching
      5.1-20 DigraphMaximumMatching
    5.2 [33X[0;0YNeighbours and degree[133X
      5.2-1 AdjacencyMatrix
      5.2-2 CharacteristicPolynomial
      5.2-3 BooleanAdjacencyMatrix
      5.2-4 DigraphAdjacencyFunction
      5.2-5 DigraphRange
      5.2-6 OutNeighbours
      5.2-7 InNeighbours
      5.2-8 OutDegrees
      5.2-9 InDegrees
      5.2-10 OutDegreeOfVertex
      5.2-11 OutNeighboursOfVertex
      5.2-12 InDegreeOfVertex
      5.2-13 InNeighboursOfVertex
      5.2-14 DigraphLoops
      5.2-15 DegreeMatrix
      5.2-16 LaplacianMatrix
    5.3 [33X[0;0YOrders[133X
      5.3-1 PartialOrderDigraphMeetOfVertices
      5.3-2 NonUpperSemimodularPair
    5.4 [33X[0;0YReachability and connectivity[133X
      5.4-1 DigraphDiameter
      5.4-2 DigraphShortestDistance
      5.4-3 DigraphShortestDistances
      5.4-4 DigraphLongestDistanceFromVertex
      5.4-5 DigraphDistanceSet
      5.4-6 DigraphGirth
      5.4-7 DigraphOddGirth
      5.4-8 DigraphUndirectedGirth
      5.4-9 DigraphConnectedComponents
      5.4-10 DigraphConnectedComponent
      5.4-11 DigraphStronglyConnectedComponents
      5.4-12 DigraphStronglyConnectedComponent
      5.4-13 DigraphBicomponents
      5.4-14 ArticulationPoints
      5.4-15 Bridges
      5.4-16 StrongOrientation
      5.4-17 DigraphPeriod
      5.4-18 DigraphFloydWarshall
      5.4-19 IsReachable
      5.4-20 IsDigraphPath
      5.4-21 VerticesReachableFrom
      5.4-22 DigraphPath
      5.4-23 DigraphShortestPath
      5.4-24 DigraphRandomWalk
      5.4-25 DigraphAbsorptionProbabilities
      5.4-26 DigraphAbsorptionExpectedSteps
      5.4-27 Dominators
      5.4-28 DominatorTree
      5.4-29 IteratorOfPaths
      5.4-30 DigraphAllSimpleCircuits
      5.4-31 DigraphLongestSimpleCircuit
      5.4-32 DigraphAllUndirectedSimpleCircuits
      5.4-33 DigraphAllChordlessCycles
      5.4-34 DigraphLayers
      5.4-35 DigraphDegeneracy
      5.4-36 DigraphDegeneracyOrdering
      5.4-37 HamiltonianPath
      5.4-38 NrSpanningTrees
      5.4-39 DigraphDijkstra
      5.4-40 DigraphCycleBasis
    5.5 [33X[0;0YCayley graphs of groups[133X
      5.5-1 GroupOfCayleyDigraph
      5.5-2 GeneratorsOfCayleyDigraph
    5.6 [33X[0;0YAssociated semigroups[133X
      5.6-1 AsSemigroup
      5.6-2 AsSemigroup
    5.7 [33X[0;0YPlanarity[133X
      5.7-1 KuratowskiPlanarSubdigraph
      5.7-2 KuratowskiOuterPlanarSubdigraph
      5.7-3 PlanarEmbedding
      5.7-4 OuterPlanarEmbedding
      5.7-5 SubdigraphHomeomorphicToK23
    5.8 [33X[0;0YHashing[133X
      5.8-1 DigraphHash
  6 [33X[0;0YProperties of digraphs[133X
    6.1 [33X[0;0YVertex properties[133X
      6.1-1 DigraphHasAVertex
      6.1-2 DigraphHasNoVertices
    6.2 [33X[0;0YEdge properties[133X
      6.2-1 DigraphHasLoops
      6.2-2 IsAntiSymmetricDigraph
      6.2-3 IsBipartiteDigraph
      6.2-4 IsCompleteBipartiteDigraph
      6.2-5 IsCompleteDigraph
      6.2-6 IsCompleteMultipartiteDigraph
      6.2-7 IsEmptyDigraph
      6.2-8 IsEquivalenceDigraph
      6.2-9 IsFunctionalDigraph
      6.2-10 IsPermutationDigraph
      6.2-11 IsMultiDigraph
      6.2-12 IsNonemptyDigraph
      6.2-13 IsReflexiveDigraph
      6.2-14 IsSymmetricDigraph
      6.2-15 IsTournament
      6.2-16 IsTransitiveDigraph
    6.3 [33X[0;0YEdge Weights[133X
      6.3-1 EdgeWeights
      6.3-2 EdgeWeightedDigraph
      6.3-3 EdgeWeightedDigraphTotalWeight
      6.3-4 EdgeWeightedDigraphMinimumSpanningTree
    6.4 [33X[0;0YOrders[133X
      6.4-1 IsPreorderDigraph
      6.4-2 IsPartialOrderDigraph
      6.4-3 IsMeetSemilatticeDigraph
      6.4-4 DigraphMeetTable
      6.4-5 IsUpperSemimodularDigraph
      6.4-6 IsDistributiveLatticeDigraph
      6.4-7 IsModularLatticeDigraph
    6.5 [33X[0;0YRegularity[133X
      6.5-1 IsInRegularDigraph
      6.5-2 IsOutRegularDigraph
      6.5-3 IsRegularDigraph
      6.5-4 IsDistanceRegularDigraph
    6.6 [33X[0;0YConnectivity and cycles[133X
      6.6-1 IsAcyclicDigraph
      6.6-2 IsChainDigraph
      6.6-3 IsConnectedDigraph
      6.6-4 IsBiconnectedDigraph
      6.6-5 IsBridgelessDigraph
      6.6-6 IsStronglyConnectedDigraph
      6.6-7 IsAperiodicDigraph
      6.6-8 IsDirectedTree
      6.6-9 IsUndirectedTree
      6.6-10 IsEulerianDigraph
      6.6-11 IsHamiltonianDigraph
      6.6-12 IsCycleDigraph
    6.7 [33X[0;0YPlanarity[133X
      6.7-1 IsPlanarDigraph
      6.7-2 IsOuterPlanarDigraph
    6.8 [33X[0;0YHomomorphisms and transformations[133X
      6.8-1 IsDigraphCore
      6.8-2 IsEdgeTransitive
      6.8-3 IsVertexTransitive
  7 [33X[0;0YHomomorphisms[133X
    7.1 [33X[0;0YActing on digraphs[133X
      7.1-1 OnDigraphs
      7.1-2 OnMultiDigraphs
      7.1-3 OnTuplesDigraphs
    7.2 [33X[0;0YIsomorphisms and canonical labellings[133X
      7.2-1 DigraphsUseNauty
      7.2-2 AutomorphismGroup
      7.2-3 BlissAutomorphismGroup
      7.2-4 NautyAutomorphismGroup
      7.2-5 AutomorphismGroup
      7.2-6 AutomorphismGroup
      7.2-7 BlissCanonicalLabelling
      7.2-8 BlissCanonicalLabelling
      7.2-9 BlissCanonicalDigraph
      7.2-10 DigraphGroup
      7.2-11 DigraphOrbits
      7.2-12 DigraphOrbitReps
      7.2-13 DigraphSchreierVector
      7.2-14 DigraphStabilizer
      7.2-15 IsIsomorphicDigraph
      7.2-16 IsIsomorphicDigraph
      7.2-17 IsomorphismDigraphs
      7.2-18 IsomorphismDigraphs
      7.2-19 RepresentativeOutNeighbours
      7.2-20 IsDigraphIsomorphism
      7.2-21 IsDigraphColouring
      7.2-22 MaximalCommonSubdigraph
      7.2-23 MinimalCommonSuperdigraph
    7.3 [33X[0;0YHomomorphisms of digraphs[133X
      7.3-1 HomomorphismDigraphsFinder
      7.3-2 DigraphHomomorphism
      7.3-3 HomomorphismsDigraphs
      7.3-4 DigraphMonomorphism
      7.3-5 MonomorphismsDigraphs
      7.3-6 DigraphEpimorphism
      7.3-7 EpimorphismsDigraphs
      7.3-8 DigraphEmbedding
      7.3-9 EmbeddingsDigraphs
      7.3-10 IsDigraphHomomorphism
      7.3-11 IsDigraphEmbedding
      7.3-12 SubdigraphsMonomorphisms
      7.3-13 DigraphsRespectsColouring
      7.3-14 GeneratorsOfEndomorphismMonoid
      7.3-15 DigraphColouring
      7.3-16 DigraphGreedyColouring
      7.3-17 DigraphWelshPowellOrder
      7.3-18 ChromaticNumber
      7.3-19 DigraphCore
      7.3-20 LatticeDigraphEmbedding
      7.3-21 IsLatticeHomomorphism
  8 [33X[0;0YFinding cliques and independent sets[133X
    8.1 [33X[0;0YFinding cliques[133X
      8.1-1 IsClique
      8.1-2 CliquesFinder
      8.1-3 DigraphClique
      8.1-4 DigraphMaximalCliques
      8.1-5 CliqueNumber
    8.2 [33X[0;0YFinding independent sets[133X
      8.2-1 IsIndependentSet
      8.2-2 DigraphIndependentSet
      8.2-3 DigraphMaximalIndependentSets
  9 [33X[0;0YVisualising and IO[133X
    9.1 [33X[0;0YVisualising a digraph[133X
      9.1-1 Splash
      9.1-2 DotDigraph
      9.1-3 DotSymmetricDigraph
      9.1-4 DotPartialOrderDigraph
      9.1-5 DotPreorderDigraph
      9.1-6 DotHighlightedDigraph
    9.2 [33X[0;0YReading and writing digraphs to a file[133X
      9.2-1 String
      9.2-2 DigraphFromGraph6String
      9.2-3 Graph6String
      9.2-4 DigraphFile
      9.2-5 ReadDigraphs
      9.2-6 WriteDigraphs
      9.2-7 IteratorFromDigraphFile
      9.2-8 DigraphPlainTextLineEncoder
      9.2-9 TournamentLineDecoder
      9.2-10 AdjacencyMatrixUpperTriangleLineDecoder
      9.2-11 TCodeDecoder
      9.2-12 PlainTextString
      9.2-13 WritePlainTextDigraph
      9.2-14 WriteDIMACSDigraph
  A [33X[0;0YGrape to Digraphs Command Map[133X
    A.1 [33X[0;0YFunctions to construct and modify graphs[133X
    A.2 [33X[0;0YFunctions to inspect graphs, vertices and edges[133X
    A.3 [33X[0;0YFunctions to determine regularity properties of graphs[133X
    A.4 [33X[0;0YSome special vertex subsets of a graph[133X
    A.5 [33X[0;0YFunctions to construct new graphs from old[133X
    A.6 [33X[0;0YVertex-Colouring and Complete Subgraphs[133X
    A.7 [33X[0;0YAutomorphism groups and isomorphism testing for graphs[133X
  
  
  [32X
