\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{ The \textsf {Digraphs} package }}{5}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{Introduction}}{5}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{Definitions}}{6}{subsection.1.1.1}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Installing \textsf {Digraphs}}}{8}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{For those in a hurry}}{8}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{Configuration options}}{9}{subsection.2.1.1}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Optional package dependencies}}{9}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{The Grape package}}{9}{subsection.2.2.1}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{Compiling the kernel module}}{10}{section.2.3}%
\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{Rebuilding the documentation}}{10}{section.2.4}%
\contentsline {subsection}{\numberline {2.4.1}\textcolor {Chapter }{DigraphsMakeDoc}}{10}{subsection.2.4.1}%
\contentsline {section}{\numberline {2.5}\textcolor {Chapter }{Testing your installation}}{10}{section.2.5}%
\contentsline {subsection}{\numberline {2.5.1}\textcolor {Chapter }{DigraphsTestInstall}}{11}{subsection.2.5.1}%
\contentsline {subsection}{\numberline {2.5.2}\textcolor {Chapter }{DigraphsTestStandard}}{11}{subsection.2.5.2}%
\contentsline {subsection}{\numberline {2.5.3}\textcolor {Chapter }{DigraphsTestExtreme}}{11}{subsection.2.5.3}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Creating digraphs}}{12}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Creating digraphs}}{12}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{IsDigraph}}{12}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {3.1.2}\textcolor {Chapter }{IsMutableDigraph}}{12}{subsection.3.1.2}%
\contentsline {subsection}{\numberline {3.1.3}\textcolor {Chapter }{IsImmutableDigraph}}{12}{subsection.3.1.3}%
\contentsline {subsection}{\numberline {3.1.4}\textcolor {Chapter }{IsCayleyDigraph}}{13}{subsection.3.1.4}%
\contentsline {subsection}{\numberline {3.1.5}\textcolor {Chapter }{IsDigraphWithAdjacencyFunction}}{13}{subsection.3.1.5}%
\contentsline {subsection}{\numberline {3.1.6}\textcolor {Chapter }{DigraphByOutNeighboursType}}{13}{subsection.3.1.6}%
\contentsline {subsection}{\numberline {3.1.7}\textcolor {Chapter }{Digraph}}{13}{subsection.3.1.7}%
\contentsline {subsection}{\numberline {3.1.8}\textcolor {Chapter }{DigraphByAdjacencyMatrix}}{15}{subsection.3.1.8}%
\contentsline {subsection}{\numberline {3.1.9}\textcolor {Chapter }{DigraphByEdges}}{16}{subsection.3.1.9}%
\contentsline {subsection}{\numberline {3.1.10}\textcolor {Chapter }{EdgeOrbitsDigraph}}{17}{subsection.3.1.10}%
\contentsline {subsection}{\numberline {3.1.11}\textcolor {Chapter }{DigraphByInNeighbours}}{17}{subsection.3.1.11}%
\contentsline {subsection}{\numberline {3.1.12}\textcolor {Chapter }{CayleyDigraph}}{18}{subsection.3.1.12}%
\contentsline {subsection}{\numberline {3.1.13}\textcolor {Chapter }{ListNamedDigraphs}}{18}{subsection.3.1.13}%
\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{Changing representations}}{19}{section.3.2}%
\contentsline {subsection}{\numberline {3.2.1}\textcolor {Chapter }{AsBinaryRelation}}{19}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {3.2.2}\textcolor {Chapter }{AsDigraph (for a binary relation)}}{19}{subsection.3.2.2}%
\contentsline {subsection}{\numberline {3.2.3}\textcolor {Chapter }{Graph}}{20}{subsection.3.2.3}%
\contentsline {subsection}{\numberline {3.2.4}\textcolor {Chapter }{AsGraph}}{21}{subsection.3.2.4}%
\contentsline {subsection}{\numberline {3.2.5}\textcolor {Chapter }{AsTransformation}}{21}{subsection.3.2.5}%
\contentsline {section}{\numberline {3.3}\textcolor {Chapter }{New digraphs from old}}{22}{section.3.3}%
\contentsline {subsection}{\numberline {3.3.1}\textcolor {Chapter }{DigraphImmutableCopy}}{22}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {3.3.2}\textcolor {Chapter }{DigraphImmutableCopyIfImmutable}}{22}{subsection.3.3.2}%
\contentsline {subsection}{\numberline {3.3.3}\textcolor {Chapter }{InducedSubdigraph}}{23}{subsection.3.3.3}%
\contentsline {subsection}{\numberline {3.3.4}\textcolor {Chapter }{ReducedDigraph}}{24}{subsection.3.3.4}%
\contentsline {subsection}{\numberline {3.3.5}\textcolor {Chapter }{MaximalSymmetricSubdigraph}}{24}{subsection.3.3.5}%
\contentsline {subsection}{\numberline {3.3.6}\textcolor {Chapter }{MaximalAntiSymmetricSubdigraph}}{25}{subsection.3.3.6}%
\contentsline {subsection}{\numberline {3.3.7}\textcolor {Chapter }{UndirectedSpanningForest}}{26}{subsection.3.3.7}%
\contentsline {subsection}{\numberline {3.3.8}\textcolor {Chapter }{DigraphShortestPathSpanningTree}}{27}{subsection.3.3.8}%
\contentsline {subsection}{\numberline {3.3.9}\textcolor {Chapter }{QuotientDigraph}}{27}{subsection.3.3.9}%
\contentsline {subsection}{\numberline {3.3.10}\textcolor {Chapter }{DigraphReverse}}{28}{subsection.3.3.10}%
\contentsline {subsection}{\numberline {3.3.11}\textcolor {Chapter }{DigraphDual}}{29}{subsection.3.3.11}%
\contentsline {subsection}{\numberline {3.3.12}\textcolor {Chapter }{DigraphSymmetricClosure}}{29}{subsection.3.3.12}%
\contentsline {subsection}{\numberline {3.3.13}\textcolor {Chapter }{DigraphTransitiveClosure}}{30}{subsection.3.3.13}%
\contentsline {subsection}{\numberline {3.3.14}\textcolor {Chapter }{DigraphTransitiveReduction}}{31}{subsection.3.3.14}%
\contentsline {subsection}{\numberline {3.3.15}\textcolor {Chapter }{DigraphAddVertex}}{32}{subsection.3.3.15}%
\contentsline {subsection}{\numberline {3.3.16}\textcolor {Chapter }{DigraphAddVertices (for a digraph and an integer)}}{32}{subsection.3.3.16}%
\contentsline {subsection}{\numberline {3.3.17}\textcolor {Chapter }{DigraphAddEdge (for a digraph and an edge)}}{33}{subsection.3.3.17}%
\contentsline {subsection}{\numberline {3.3.18}\textcolor {Chapter }{DigraphAddEdgeOrbit}}{34}{subsection.3.3.18}%
\contentsline {subsection}{\numberline {3.3.19}\textcolor {Chapter }{DigraphAddEdges}}{34}{subsection.3.3.19}%
\contentsline {subsection}{\numberline {3.3.20}\textcolor {Chapter }{DigraphRemoveVertex}}{35}{subsection.3.3.20}%
\contentsline {subsection}{\numberline {3.3.21}\textcolor {Chapter }{DigraphRemoveVertices}}{36}{subsection.3.3.21}%
\contentsline {subsection}{\numberline {3.3.22}\textcolor {Chapter }{DigraphRemoveEdge (for a digraph and an edge)}}{36}{subsection.3.3.22}%
\contentsline {subsection}{\numberline {3.3.23}\textcolor {Chapter }{DigraphRemoveEdgeOrbit}}{37}{subsection.3.3.23}%
\contentsline {subsection}{\numberline {3.3.24}\textcolor {Chapter }{DigraphRemoveEdges}}{38}{subsection.3.3.24}%
\contentsline {subsection}{\numberline {3.3.25}\textcolor {Chapter }{DigraphRemoveLoops}}{38}{subsection.3.3.25}%
\contentsline {subsection}{\numberline {3.3.26}\textcolor {Chapter }{DigraphRemoveAllMultipleEdges}}{39}{subsection.3.3.26}%
\contentsline {subsection}{\numberline {3.3.27}\textcolor {Chapter }{DigraphContractEdge (for a digraph and a list of positive integers)}}{39}{subsection.3.3.27}%
\contentsline {subsection}{\numberline {3.3.28}\textcolor {Chapter }{DigraphReverseEdges (for a digraph and a list of edges)}}{40}{subsection.3.3.28}%
\contentsline {subsection}{\numberline {3.3.29}\textcolor {Chapter }{DigraphDisjointUnion (for an arbitrary number of digraphs)}}{40}{subsection.3.3.29}%
\contentsline {subsection}{\numberline {3.3.30}\textcolor {Chapter }{DigraphEdgeUnion (for a positive number of digraphs)}}{41}{subsection.3.3.30}%
\contentsline {subsection}{\numberline {3.3.31}\textcolor {Chapter }{DigraphJoin (for a positive number of digraphs)}}{42}{subsection.3.3.31}%
\contentsline {subsection}{\numberline {3.3.32}\textcolor {Chapter }{DigraphCartesianProduct (for a positive number of digraphs)}}{42}{subsection.3.3.32}%
\contentsline {subsection}{\numberline {3.3.33}\textcolor {Chapter }{DigraphDirectProduct (for a positive number of digraphs)}}{43}{subsection.3.3.33}%
\contentsline {subsection}{\numberline {3.3.34}\textcolor {Chapter }{ConormalProduct}}{44}{subsection.3.3.34}%
\contentsline {subsection}{\numberline {3.3.35}\textcolor {Chapter }{HomomorphicProduct}}{44}{subsection.3.3.35}%
\contentsline {subsection}{\numberline {3.3.36}\textcolor {Chapter }{LexicographicProduct}}{45}{subsection.3.3.36}%
\contentsline {subsection}{\numberline {3.3.37}\textcolor {Chapter }{ModularProduct}}{45}{subsection.3.3.37}%
\contentsline {subsection}{\numberline {3.3.38}\textcolor {Chapter }{StrongProduct}}{46}{subsection.3.3.38}%
\contentsline {subsection}{\numberline {3.3.39}\textcolor {Chapter }{DigraphCartesianProductProjections}}{46}{subsection.3.3.39}%
\contentsline {subsection}{\numberline {3.3.40}\textcolor {Chapter }{DigraphDirectProductProjections}}{47}{subsection.3.3.40}%
\contentsline {subsection}{\numberline {3.3.41}\textcolor {Chapter }{LineDigraph}}{47}{subsection.3.3.41}%
\contentsline {subsection}{\numberline {3.3.42}\textcolor {Chapter }{LineUndirectedDigraph}}{48}{subsection.3.3.42}%
\contentsline {subsection}{\numberline {3.3.43}\textcolor {Chapter }{DoubleDigraph}}{48}{subsection.3.3.43}%
\contentsline {subsection}{\numberline {3.3.44}\textcolor {Chapter }{BipartiteDoubleDigraph}}{48}{subsection.3.3.44}%
\contentsline {subsection}{\numberline {3.3.45}\textcolor {Chapter }{DigraphAddAllLoops}}{49}{subsection.3.3.45}%
\contentsline {subsection}{\numberline {3.3.46}\textcolor {Chapter }{DistanceDigraph (for digraph and int)}}{49}{subsection.3.3.46}%
\contentsline {subsection}{\numberline {3.3.47}\textcolor {Chapter }{DigraphClosure}}{50}{subsection.3.3.47}%
\contentsline {subsection}{\numberline {3.3.48}\textcolor {Chapter }{DigraphMycielskian}}{50}{subsection.3.3.48}%
\contentsline {section}{\numberline {3.4}\textcolor {Chapter }{Random digraphs}}{51}{section.3.4}%
\contentsline {subsection}{\numberline {3.4.1}\textcolor {Chapter }{RandomDigraph}}{51}{subsection.3.4.1}%
\contentsline {subsection}{\numberline {3.4.2}\textcolor {Chapter }{RandomMultiDigraph}}{52}{subsection.3.4.2}%
\contentsline {subsection}{\numberline {3.4.3}\textcolor {Chapter }{RandomTournament}}{52}{subsection.3.4.3}%
\contentsline {subsection}{\numberline {3.4.4}\textcolor {Chapter }{RandomLattice}}{53}{subsection.3.4.4}%
\contentsline {section}{\numberline {3.5}\textcolor {Chapter }{Standard examples}}{53}{section.3.5}%
\contentsline {subsection}{\numberline {3.5.1}\textcolor {Chapter }{AndrasfaiGraph}}{53}{subsection.3.5.1}%
\contentsline {subsection}{\numberline {3.5.2}\textcolor {Chapter }{BananaTree}}{54}{subsection.3.5.2}%
\contentsline {subsection}{\numberline {3.5.3}\textcolor {Chapter }{BinaryTree}}{54}{subsection.3.5.3}%
\contentsline {subsection}{\numberline {3.5.4}\textcolor {Chapter }{BinomialTreeGraph}}{55}{subsection.3.5.4}%
\contentsline {subsection}{\numberline {3.5.5}\textcolor {Chapter }{BishopsGraph}}{55}{subsection.3.5.5}%
\contentsline {subsection}{\numberline {3.5.6}\textcolor {Chapter }{BondyGraph}}{56}{subsection.3.5.6}%
\contentsline {subsection}{\numberline {3.5.7}\textcolor {Chapter }{BookGraph}}{57}{subsection.3.5.7}%
\contentsline {subsection}{\numberline {3.5.8}\textcolor {Chapter }{StackedBookGraph}}{57}{subsection.3.5.8}%
\contentsline {subsection}{\numberline {3.5.9}\textcolor {Chapter }{ChainDigraph}}{58}{subsection.3.5.9}%
\contentsline {subsection}{\numberline {3.5.10}\textcolor {Chapter }{CirculantGraph}}{58}{subsection.3.5.10}%
\contentsline {subsection}{\numberline {3.5.11}\textcolor {Chapter }{CompleteDigraph}}{59}{subsection.3.5.11}%
\contentsline {subsection}{\numberline {3.5.12}\textcolor {Chapter }{CompleteBipartiteDigraph}}{59}{subsection.3.5.12}%
\contentsline {subsection}{\numberline {3.5.13}\textcolor {Chapter }{CompleteMultipartiteDigraph}}{59}{subsection.3.5.13}%
\contentsline {subsection}{\numberline {3.5.14}\textcolor {Chapter }{CycleDigraph}}{60}{subsection.3.5.14}%
\contentsline {subsection}{\numberline {3.5.15}\textcolor {Chapter }{CycleGraph}}{60}{subsection.3.5.15}%
\contentsline {subsection}{\numberline {3.5.16}\textcolor {Chapter }{EmptyDigraph}}{61}{subsection.3.5.16}%
\contentsline {subsection}{\numberline {3.5.17}\textcolor {Chapter }{GearGraph}}{61}{subsection.3.5.17}%
\contentsline {subsection}{\numberline {3.5.18}\textcolor {Chapter }{HaarGraph}}{62}{subsection.3.5.18}%
\contentsline {subsection}{\numberline {3.5.19}\textcolor {Chapter }{HalvedCubeGraph}}{62}{subsection.3.5.19}%
\contentsline {subsection}{\numberline {3.5.20}\textcolor {Chapter }{HanoiGraph}}{63}{subsection.3.5.20}%
\contentsline {subsection}{\numberline {3.5.21}\textcolor {Chapter }{HelmGraph}}{63}{subsection.3.5.21}%
\contentsline {subsection}{\numberline {3.5.22}\textcolor {Chapter }{HypercubeGraph}}{64}{subsection.3.5.22}%
\contentsline {subsection}{\numberline {3.5.23}\textcolor {Chapter }{JohnsonDigraph}}{64}{subsection.3.5.23}%
\contentsline {subsection}{\numberline {3.5.24}\textcolor {Chapter }{KellerGraph}}{65}{subsection.3.5.24}%
\contentsline {subsection}{\numberline {3.5.25}\textcolor {Chapter }{KingsGraph}}{65}{subsection.3.5.25}%
\contentsline {subsection}{\numberline {3.5.26}\textcolor {Chapter }{KneserGraph}}{66}{subsection.3.5.26}%
\contentsline {subsection}{\numberline {3.5.27}\textcolor {Chapter }{KnightsGraph}}{67}{subsection.3.5.27}%
\contentsline {subsection}{\numberline {3.5.28}\textcolor {Chapter }{LindgrenSousselierGraph}}{67}{subsection.3.5.28}%
\contentsline {subsection}{\numberline {3.5.29}\textcolor {Chapter }{LollipopGraph}}{68}{subsection.3.5.29}%
\contentsline {subsection}{\numberline {3.5.30}\textcolor {Chapter }{MobiusLadderGraph}}{68}{subsection.3.5.30}%
\contentsline {subsection}{\numberline {3.5.31}\textcolor {Chapter }{MycielskiGraph}}{69}{subsection.3.5.31}%
\contentsline {subsection}{\numberline {3.5.32}\textcolor {Chapter }{OddGraph}}{70}{subsection.3.5.32}%
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\contentsline {subsection}{\numberline {3.5.34}\textcolor {Chapter }{PermutationStarGraph}}{70}{subsection.3.5.34}%
\contentsline {subsection}{\numberline {3.5.35}\textcolor {Chapter }{PetersenGraph}}{71}{subsection.3.5.35}%
\contentsline {subsection}{\numberline {3.5.36}\textcolor {Chapter }{GeneralisedPetersenGraph}}{71}{subsection.3.5.36}%
\contentsline {subsection}{\numberline {3.5.37}\textcolor {Chapter }{PrismGraph}}{72}{subsection.3.5.37}%
\contentsline {subsection}{\numberline {3.5.38}\textcolor {Chapter }{StackedPrismGraph}}{73}{subsection.3.5.38}%
\contentsline {subsection}{\numberline {3.5.39}\textcolor {Chapter }{QueensGraph}}{73}{subsection.3.5.39}%
\contentsline {subsection}{\numberline {3.5.40}\textcolor {Chapter }{RooksGraph}}{74}{subsection.3.5.40}%
\contentsline {subsection}{\numberline {3.5.41}\textcolor {Chapter }{SquareGridGraph}}{75}{subsection.3.5.41}%
\contentsline {subsection}{\numberline {3.5.42}\textcolor {Chapter }{TriangularGridGraph}}{75}{subsection.3.5.42}%
\contentsline {subsection}{\numberline {3.5.43}\textcolor {Chapter }{StarGraph}}{76}{subsection.3.5.43}%
\contentsline {subsection}{\numberline {3.5.44}\textcolor {Chapter }{TadpoleGraph}}{76}{subsection.3.5.44}%
\contentsline {subsection}{\numberline {3.5.45}\textcolor {Chapter }{WalshHadamardGraph}}{77}{subsection.3.5.45}%
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\contentsline {subsection}{\numberline {3.5.48}\textcolor {Chapter }{WindmillGraph}}{78}{subsection.3.5.48}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Operators}}{79}{chapter.4}%
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\contentsline {chapter}{\numberline {5}\textcolor {Chapter }{Attributes and operations}}{82}{chapter.5}%
\contentsline {section}{\numberline {5.1}\textcolor {Chapter }{Vertices and edges}}{82}{section.5.1}%
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\contentsline {subsection}{\numberline {5.1.2}\textcolor {Chapter }{DigraphNrVertices}}{82}{subsection.5.1.2}%
\contentsline {subsection}{\numberline {5.1.3}\textcolor {Chapter }{DigraphEdges}}{83}{subsection.5.1.3}%
\contentsline {subsection}{\numberline {5.1.4}\textcolor {Chapter }{DigraphNrEdges}}{83}{subsection.5.1.4}%
\contentsline {subsection}{\numberline {5.1.5}\textcolor {Chapter }{DigraphNrAdjacencies}}{84}{subsection.5.1.5}%
\contentsline {subsection}{\numberline {5.1.6}\textcolor {Chapter }{DigraphNrAdjacenciesWithoutLoops}}{84}{subsection.5.1.6}%
\contentsline {subsection}{\numberline {5.1.7}\textcolor {Chapter }{DigraphNrLoops}}{85}{subsection.5.1.7}%
\contentsline {subsection}{\numberline {5.1.8}\textcolor {Chapter }{DigraphSinks}}{85}{subsection.5.1.8}%
\contentsline {subsection}{\numberline {5.1.9}\textcolor {Chapter }{DigraphSources}}{85}{subsection.5.1.9}%
\contentsline {subsection}{\numberline {5.1.10}\textcolor {Chapter }{DigraphTopologicalSort}}{86}{subsection.5.1.10}%
\contentsline {subsection}{\numberline {5.1.11}\textcolor {Chapter }{DigraphVertexLabel}}{86}{subsection.5.1.11}%
\contentsline {subsection}{\numberline {5.1.12}\textcolor {Chapter }{DigraphVertexLabels}}{87}{subsection.5.1.12}%
\contentsline {subsection}{\numberline {5.1.13}\textcolor {Chapter }{DigraphEdgeLabel}}{88}{subsection.5.1.13}%
\contentsline {subsection}{\numberline {5.1.14}\textcolor {Chapter }{DigraphEdgeLabels}}{88}{subsection.5.1.14}%
\contentsline {subsection}{\numberline {5.1.15}\textcolor {Chapter }{DigraphInEdges}}{89}{subsection.5.1.15}%
\contentsline {subsection}{\numberline {5.1.16}\textcolor {Chapter }{DigraphOutEdges}}{90}{subsection.5.1.16}%
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\contentsline {subsection}{\numberline {5.1.19}\textcolor {Chapter }{DigraphMaximalMatching}}{91}{subsection.5.1.19}%
\contentsline {subsection}{\numberline {5.1.20}\textcolor {Chapter }{DigraphMaximumMatching}}{91}{subsection.5.1.20}%
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\contentsline {subsection}{\numberline {5.2.2}\textcolor {Chapter }{CharacteristicPolynomial}}{93}{subsection.5.2.2}%
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\contentsline {subsection}{\numberline {5.2.5}\textcolor {Chapter }{DigraphRange}}{95}{subsection.5.2.5}%
\contentsline {subsection}{\numberline {5.2.6}\textcolor {Chapter }{OutNeighbours}}{95}{subsection.5.2.6}%
\contentsline {subsection}{\numberline {5.2.7}\textcolor {Chapter }{InNeighbours}}{96}{subsection.5.2.7}%
\contentsline {subsection}{\numberline {5.2.8}\textcolor {Chapter }{OutDegrees}}{97}{subsection.5.2.8}%
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\contentsline {subsection}{\numberline {5.2.10}\textcolor {Chapter }{OutDegreeOfVertex}}{98}{subsection.5.2.10}%
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\contentsline {subsection}{\numberline {5.2.15}\textcolor {Chapter }{DegreeMatrix}}{100}{subsection.5.2.15}%
\contentsline {subsection}{\numberline {5.2.16}\textcolor {Chapter }{LaplacianMatrix}}{101}{subsection.5.2.16}%
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\contentsline {subsection}{\numberline {5.3.2}\textcolor {Chapter }{NonUpperSemimodularPair}}{102}{subsection.5.3.2}%
\contentsline {section}{\numberline {5.4}\textcolor {Chapter }{Reachability and connectivity}}{102}{section.5.4}%
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\contentsline {subsection}{\numberline {5.4.4}\textcolor {Chapter }{DigraphLongestDistanceFromVertex}}{104}{subsection.5.4.4}%
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\contentsline {subsection}{\numberline {5.4.6}\textcolor {Chapter }{DigraphGirth}}{105}{subsection.5.4.6}%
\contentsline {subsection}{\numberline {5.4.7}\textcolor {Chapter }{DigraphOddGirth}}{106}{subsection.5.4.7}%
\contentsline {subsection}{\numberline {5.4.8}\textcolor {Chapter }{DigraphUndirectedGirth}}{106}{subsection.5.4.8}%
\contentsline {subsection}{\numberline {5.4.9}\textcolor {Chapter }{DigraphConnectedComponents}}{107}{subsection.5.4.9}%
\contentsline {subsection}{\numberline {5.4.10}\textcolor {Chapter }{DigraphConnectedComponent}}{108}{subsection.5.4.10}%
\contentsline {subsection}{\numberline {5.4.11}\textcolor {Chapter }{DigraphStronglyConnectedComponents}}{108}{subsection.5.4.11}%
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\contentsline {subsection}{\numberline {5.4.13}\textcolor {Chapter }{DigraphBicomponents}}{109}{subsection.5.4.13}%
\contentsline {subsection}{\numberline {5.4.14}\textcolor {Chapter }{ArticulationPoints}}{110}{subsection.5.4.14}%
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\contentsline {subsection}{\numberline {5.4.17}\textcolor {Chapter }{DigraphPeriod}}{112}{subsection.5.4.17}%
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\contentsline {subsection}{\numberline {6.6.11}\textcolor {Chapter }{IsHamiltonianDigraph}}{157}{subsection.6.6.11}%
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\contentsline {subsection}{\numberline {6.8.3}\textcolor {Chapter }{IsVertexTransitive}}{160}{subsection.6.8.3}%
\contentsline {chapter}{\numberline {7}\textcolor {Chapter }{Homomorphisms}}{161}{chapter.7}%
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\contentsline {subsection}{\numberline {7.1.2}\textcolor {Chapter }{OnMultiDigraphs}}{162}{subsection.7.1.2}%
\contentsline {subsection}{\numberline {7.1.3}\textcolor {Chapter }{OnTuplesDigraphs (for a list of digraphs and a perm)}}{162}{subsection.7.1.3}%
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\contentsline {subsection}{\numberline {7.2.2}\textcolor {Chapter }{AutomorphismGroup (for a digraph)}}{163}{subsection.7.2.2}%
\contentsline {subsection}{\numberline {7.2.3}\textcolor {Chapter }{BlissAutomorphismGroup (for a digraph)}}{164}{subsection.7.2.3}%
\contentsline {subsection}{\numberline {7.2.4}\textcolor {Chapter }{NautyAutomorphismGroup}}{165}{subsection.7.2.4}%
\contentsline {subsection}{\numberline {7.2.5}\textcolor {Chapter }{AutomorphismGroup (for a digraph and a homogeneous list)}}{165}{subsection.7.2.5}%
\contentsline {subsection}{\numberline {7.2.6}\textcolor {Chapter }{AutomorphismGroup (for a digraph, homogeneous list, and list)}}{166}{subsection.7.2.6}%
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\contentsline {subsection}{\numberline {7.2.10}\textcolor {Chapter }{DigraphGroup}}{170}{subsection.7.2.10}%
\contentsline {subsection}{\numberline {7.2.11}\textcolor {Chapter }{DigraphOrbits}}{171}{subsection.7.2.11}%
\contentsline {subsection}{\numberline {7.2.12}\textcolor {Chapter }{DigraphOrbitReps}}{171}{subsection.7.2.12}%
\contentsline {subsection}{\numberline {7.2.13}\textcolor {Chapter }{DigraphSchreierVector}}{172}{subsection.7.2.13}%
\contentsline {subsection}{\numberline {7.2.14}\textcolor {Chapter }{DigraphStabilizer}}{172}{subsection.7.2.14}%
\contentsline {subsection}{\numberline {7.2.15}\textcolor {Chapter }{IsIsomorphicDigraph (for digraphs)}}{173}{subsection.7.2.15}%
\contentsline {subsection}{\numberline {7.2.16}\textcolor {Chapter }{IsIsomorphicDigraph (for digraphs and homogeneous lists)}}{173}{subsection.7.2.16}%
\contentsline {subsection}{\numberline {7.2.17}\textcolor {Chapter }{IsomorphismDigraphs (for digraphs)}}{174}{subsection.7.2.17}%
\contentsline {subsection}{\numberline {7.2.18}\textcolor {Chapter }{IsomorphismDigraphs (for digraphs and homogeneous lists)}}{175}{subsection.7.2.18}%
\contentsline {subsection}{\numberline {7.2.19}\textcolor {Chapter }{RepresentativeOutNeighbours}}{176}{subsection.7.2.19}%
\contentsline {subsection}{\numberline {7.2.20}\textcolor {Chapter }{IsDigraphIsomorphism (for digraphs and transformation or permutation)}}{177}{subsection.7.2.20}%
\contentsline {subsection}{\numberline {7.2.21}\textcolor {Chapter }{IsDigraphColouring}}{178}{subsection.7.2.21}%
\contentsline {subsection}{\numberline {7.2.22}\textcolor {Chapter }{MaximalCommonSubdigraph}}{178}{subsection.7.2.22}%
\contentsline {subsection}{\numberline {7.2.23}\textcolor {Chapter }{MinimalCommonSuperdigraph}}{179}{subsection.7.2.23}%
\contentsline {section}{\numberline {7.3}\textcolor {Chapter }{Homomorphisms of digraphs}}{179}{section.7.3}%
\contentsline {subsection}{\numberline {7.3.1}\textcolor {Chapter }{HomomorphismDigraphsFinder}}{179}{subsection.7.3.1}%
\contentsline {subsection}{\numberline {7.3.2}\textcolor {Chapter }{DigraphHomomorphism}}{182}{subsection.7.3.2}%
\contentsline {subsection}{\numberline {7.3.3}\textcolor {Chapter }{HomomorphismsDigraphs}}{182}{subsection.7.3.3}%
\contentsline {subsection}{\numberline {7.3.4}\textcolor {Chapter }{DigraphMonomorphism}}{183}{subsection.7.3.4}%
\contentsline {subsection}{\numberline {7.3.5}\textcolor {Chapter }{MonomorphismsDigraphs}}{183}{subsection.7.3.5}%
\contentsline {subsection}{\numberline {7.3.6}\textcolor {Chapter }{DigraphEpimorphism}}{183}{subsection.7.3.6}%
\contentsline {subsection}{\numberline {7.3.7}\textcolor {Chapter }{EpimorphismsDigraphs}}{184}{subsection.7.3.7}%
\contentsline {subsection}{\numberline {7.3.8}\textcolor {Chapter }{DigraphEmbedding}}{184}{subsection.7.3.8}%
\contentsline {subsection}{\numberline {7.3.9}\textcolor {Chapter }{EmbeddingsDigraphs}}{185}{subsection.7.3.9}%
\contentsline {subsection}{\numberline {7.3.10}\textcolor {Chapter }{IsDigraphHomomorphism (for digraphs and a permutation or transformation)}}{185}{subsection.7.3.10}%
\contentsline {subsection}{\numberline {7.3.11}\textcolor {Chapter }{IsDigraphEmbedding (for digraphs and a permutation or transformation)}}{187}{subsection.7.3.11}%
\contentsline {subsection}{\numberline {7.3.12}\textcolor {Chapter }{SubdigraphsMonomorphisms}}{187}{subsection.7.3.12}%
\contentsline {subsection}{\numberline {7.3.13}\textcolor {Chapter }{DigraphsRespectsColouring}}{188}{subsection.7.3.13}%
\contentsline {subsection}{\numberline {7.3.14}\textcolor {Chapter }{GeneratorsOfEndomorphismMonoid}}{188}{subsection.7.3.14}%
\contentsline {subsection}{\numberline {7.3.15}\textcolor {Chapter }{DigraphColouring (for a digraph and a number of colours)}}{189}{subsection.7.3.15}%
\contentsline {subsection}{\numberline {7.3.16}\textcolor {Chapter }{DigraphGreedyColouring (for a digraph and vertex order)}}{190}{subsection.7.3.16}%
\contentsline {subsection}{\numberline {7.3.17}\textcolor {Chapter }{DigraphWelshPowellOrder}}{190}{subsection.7.3.17}%
\contentsline {subsection}{\numberline {7.3.18}\textcolor {Chapter }{ChromaticNumber}}{190}{subsection.7.3.18}%
\contentsline {subsection}{\numberline {7.3.19}\textcolor {Chapter }{DigraphCore}}{191}{subsection.7.3.19}%
\contentsline {subsection}{\numberline {7.3.20}\textcolor {Chapter }{LatticeDigraphEmbedding}}{191}{subsection.7.3.20}%
\contentsline {subsection}{\numberline {7.3.21}\textcolor {Chapter }{IsLatticeHomomorphism (for digraphs and a permutation or transformation)}}{192}{subsection.7.3.21}%
\contentsline {chapter}{\numberline {8}\textcolor {Chapter }{Finding cliques and independent sets}}{194}{chapter.8}%
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\contentsline {subsection}{\numberline {8.1.2}\textcolor {Chapter }{CliquesFinder}}{196}{subsection.8.1.2}%
\contentsline {subsection}{\numberline {8.1.3}\textcolor {Chapter }{DigraphClique}}{198}{subsection.8.1.3}%
\contentsline {subsection}{\numberline {8.1.4}\textcolor {Chapter }{DigraphMaximalCliques}}{199}{subsection.8.1.4}%
\contentsline {subsection}{\numberline {8.1.5}\textcolor {Chapter }{CliqueNumber}}{200}{subsection.8.1.5}%
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\contentsline {subsection}{\numberline {8.2.2}\textcolor {Chapter }{DigraphIndependentSet}}{201}{subsection.8.2.2}%
\contentsline {subsection}{\numberline {8.2.3}\textcolor {Chapter }{DigraphMaximalIndependentSets}}{203}{subsection.8.2.3}%
\contentsline {chapter}{\numberline {9}\textcolor {Chapter }{Visualising and IO}}{205}{chapter.9}%
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\contentsline {subsection}{\numberline {9.2.2}\textcolor {Chapter }{DigraphFromGraph6String}}{215}{subsection.9.2.2}%
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\contentsline {subsection}{\numberline {9.2.5}\textcolor {Chapter }{ReadDigraphs}}{217}{subsection.9.2.5}%
\contentsline {subsection}{\numberline {9.2.6}\textcolor {Chapter }{WriteDigraphs}}{219}{subsection.9.2.6}%
\contentsline {subsection}{\numberline {9.2.7}\textcolor {Chapter }{IteratorFromDigraphFile}}{220}{subsection.9.2.7}%
\contentsline {subsection}{\numberline {9.2.8}\textcolor {Chapter }{DigraphPlainTextLineEncoder}}{221}{subsection.9.2.8}%
\contentsline {subsection}{\numberline {9.2.9}\textcolor {Chapter }{TournamentLineDecoder}}{221}{subsection.9.2.9}%
\contentsline {subsection}{\numberline {9.2.10}\textcolor {Chapter }{AdjacencyMatrixUpperTriangleLineDecoder}}{222}{subsection.9.2.10}%
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\contentsline {subsection}{\numberline {9.2.12}\textcolor {Chapter }{PlainTextString}}{223}{subsection.9.2.12}%
\contentsline {subsection}{\numberline {9.2.13}\textcolor {Chapter }{WritePlainTextDigraph}}{223}{subsection.9.2.13}%
\contentsline {subsection}{\numberline {9.2.14}\textcolor {Chapter }{WriteDIMACSDigraph}}{224}{subsection.9.2.14}%
\contentsline {chapter}{\numberline {A}\textcolor {Chapter }{ Grape to Digraphs Command Map }}{226}{appendix.A}%
\contentsline {section}{\numberline {A.1}\textcolor {Chapter }{ Functions to construct and modify graphs }}{226}{section.A.1}%
\contentsline {section}{\numberline {A.2}\textcolor {Chapter }{ Functions to inspect graphs, vertices and edges }}{226}{section.A.2}%
\contentsline {section}{\numberline {A.3}\textcolor {Chapter }{ Functions to determine regularity properties of graphs }}{227}{section.A.3}%
\contentsline {section}{\numberline {A.4}\textcolor {Chapter }{ Some special vertex subsets of a graph }}{227}{section.A.4}%
\contentsline {section}{\numberline {A.5}\textcolor {Chapter }{ Functions to construct new graphs from old }}{228}{section.A.5}%
\contentsline {section}{\numberline {A.6}\textcolor {Chapter }{ Vertex-Colouring and Complete Subgraphs }}{228}{section.A.6}%
\contentsline {section}{\numberline {A.7}\textcolor {Chapter }{ Automorphism groups and isomorphism testing for graphs }}{228}{section.A.7}%
\contentsline {chapter}{References}{230}{appendix*.5}%
\contentsline {chapter}{Index}{231}{section*.6}%
