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/a> <a href="chap1_mj.html" >1 </a> <a href="chap2_mj.html" >2 </a> <a href="chap3_mj.html" >3 </a> <a href="chap4_mj.html" >4 </a> <a href="chap5_mj.html" >5 </a> <a href="chap6_mj.html" >6 </a> <a href="chap7_mj.html" >7 </a> <a href="chap8_mj.html" >8 </a> <a href="chap9_mj.html" >9 </a> <a href="chapA_mj.html" >A</a> <a href="chapB_mj.html" >B</a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >Digraphs</h1 >strong class="pkg" >GAP</strong ></h2>1 .13 .1 </p>27 September 2025 div >br />Email: <span class="URL" ><a href="mailto:jdebeule@cage.ugent.be" >jdebeule@cage.ugent.be</a></span >br />Homepage: <span class="URL" ><a href="https://researchportal.vub.be/en/persons/jan-de-beule " >https://researchportal.vub.be/en/persons/jan-de-beule</a></span >br />Address : <br />Vrije Universiteit Brussel, Vakgroep Wiskunde, Pleinlaan 2 , B - 1050 Brussels, Belgium<br />br />Email: <span class="URL" ><a href="mailto:j.jonusas@gmail.com" >j.jonusas@gmail.com</a></span br />Homepage: <span class="URL" ><a href="http://julius.jonusas.work " >http://julius.jonusas.work</a></span >br />Email: <span class="URL" ><a href="mailto:jdm3@st-andrews.ac.uk" >jdm3@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://jdbm.me " >https://jdbm.me</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:gap@wilf-wilson.net" >gap@wilf-wilson.net</a></span br />Homepage: <span class="URL" ><a href="https://wilf.me " >https://wilf.me</a></span >br />Email: <span class="URL" ><a href="mailto:mct25@st-andrews.ac.uk" >mct25@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://myoung.uk/work/ " >https://myoung.uk/work/</a></span >br />Address : <br />Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9 SX, Scotland<br />br />Email: <span class="URL" ><a href="mailto:mam49@st-andrews.ac.uk" >mam49@st-andrews.ac.uk</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:finneganlbuck@gmail.com" >finneganlbuck@gmail.com</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:stuartburrell1994@gmail.com" >stuartburrell1994@gmail.com</a></span >br />Homepage: <span class="URL" ><a href="https://stuartburrell.github.io " >https://stuartburrell.github.io</a></span >br />Email: <span class="URL" ><a href="mailto:rc234@st-andrews.ac.uk" >rc234@st-andrews.ac.uk</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:ac323@st-andrews.ac.uk" >ac323@st-andrews.ac.uk</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:tom.contileslie@gmail.com" >tom.contileslie@gmail.com</a></span >br />Homepage: <span class="URL" ><a href="https://tomcontileslie.com " >https://tomcontileslie.com</a></span >br />Email: <span class="URL" ><a href="mailto:jde1@st-andrews.ac.uk" >jde1@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://github.com/Joseph-Edwards " >https://github.com/Joseph-Edwards</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:luna.elliott142857@gmail.com" >luna.elliott142857@gmail.com</a></span >br />Homepage: <span class="URL" ><a href="https://research.manchester.ac.uk/en/persons/luna-elliott " >https://research.manchester.ac.uk/en/persons/luna-elliott</a></span >br />Email: <span class="URL" ><a href="mailto:jengelh@inai.de" >jengelh@inai.de</a></span >br />Homepage: <span class="URL" ><a href="https://inai.de " >https://inai.de</a></span >br />Email: <span class="URL" ><a href="mailto:isuruf@gmail.com" >isuruf@gmail.com</a></span >br />Email: <span class="URL" ><a href="mailto:eg207@st-andrews.ac.uk" >eg207@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:fotg1@st-andrews.ac.uk" >fotg1@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:gutsche@momo.math.rwth-aachen.de" >gutsche@momo.math.rwth-aachen.de</a></span >br />Email: <span class="URL" ><a href="mailto:seh25@st-andrews.ac.uk" >seh25@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:mhorn@rptu.de" >mhorn@rptu.de</a></span >br />Homepage: <span class="URL" ><a href="https://www.quendi.de/math " >https://www.quendi.de/math</a></span >br />Address : <br />Fachbereich Mathematik, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Straße 48 , 67663 Kaiserslautern, Germany<br />br />Email: <span class="URL" ><a href="mailto:hrj4@st-andrews.ac.uk" >hrj4@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:caj21@st-andrews.ac.uk" >caj21@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://heather.cafe/ " >https://heather.cafe/</a></span br />Address : <br />Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9 SX, Scotland<br />br />Email: <span class="URL" ><a href="mailto:zlj1@st-andrews.ac.uk" >zlj1@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:obk1@st-andrews.ac.uk" >obk1@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://olexandr-konovalov.github.io/ " >https://olexandr-konovalov.github.io/</a></span >br />Address : <br />Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9 SX, Scotland<br />br />Email: <span class="URL" ><a href="mailto:hk78@st-andrews.ac.uk" >hk78@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:ahwl1@st-andrews.ac.uk" >ahwl1@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:sm544@st-andrews.ac.uk" >sm544@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:MaxBaseCode@Gmail.Com" >MaxBaseCode@Gmail.Com</a></span >br />Email: <span class="URL" ><a href="mailto:michael@orlitzky.com" >michael@orlitzky.com</a></span >br />Homepage: <span class="URL" ><a href="https://michael.orlitzky.com/ " >https://michael.orlitzky.com/</a></span >br />Email: <span class="URL" ><a href="mailto:mp322@st-andrews.ac.uk" >mp322@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:markus.pfeiffer@morphism.de" >markus.pfeiffer@morphism.de</a></span >br />Homepage: <span class="URL" ><a href="https://markusp.morphism.de/ " >https://markusp.morphism.de/</a></span >br />Email: <span class="URL" ><a href="mailto:dp211@st-andrews.ac.uk" >dp211@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:107881923+pramothragavan@users.noreply.github.com" >107881923 +pramothragavan@users.noreply.github.com</a></span >br />Email: <span class="URL" ><a href="mailto:lr217@st-andrews.ac.uk" >lr217@st-andrews.ac.uk</a></span >br />Address : <br />Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9 SX, Scotland<br />br />Email: <span class="URL" ><a href="mailto:as305@st-and.ac.uk" >as305@st-and.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:iscott@uchicago.edu" >iscott@uchicago.edu</a></span br />Email: <span class="URL" ><a href="mailto:kks4@st-andrews.ac.uk" >kks4@st-andrews.ac.uk</a></span >br />Address : <br />Jack Cole Building, North Haugh, St Andrews, Fife, KY16 9 SX, Scotland<br />br />Email: <span class="URL" ><a href="mailto:fls3@st-andrews.ac.uk" >fls3@st-andrews.ac.uk</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:bspiers972@outlook.com" >bspiers972@outlook.com</a></span >br />Email: <span class="URL" ><a href="mailto:mt200@st-andrews.ac.uk" >mt200@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://mariatsalakou.github.io/ " >https://mariatsalakou.github.io/</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:av215@st-andrews.ac.uk" >av215@st-andrews.ac.uk</a></span >br />Email: <span class="URL" ><a href="mailto:weiss@art.rwth-aachen.de" >weiss@art.rwth-aachen.de</a></span >br />Homepage: <span class="URL" ><a href="https://bit.ly/4e6pUeP " >https://bit.ly/4 e6pUeP</a></span >br />Address : <br />Chair of Algebra and Representation Theory, Pontdriesch 10 -16 , 52062 Aachen<br br />Email: <span class="URL" ><a href="mailto:mw231@st-andrews.ac.uk" >mw231@st-andrews.ac.uk</a></span >br />Address : <br />Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9 SS, Scotland<br />br />Email: <span class="URL" ><a href="mailto:f.zickgraf@dashdos.com" >f.zickgraf@dashdos.com</a></span >"X7AA6C5737B711C89" name="X7AA6C5737B711C89" ></a></p>strong class="pkg" >Digraphs</strong > package is a <strong class="pkg" >GAP</strong > package containing methods for graphs, digraphs, and multidigraphs.</p>"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>strong class="pkg" >Digraphs</strong > is free software; you can redistribute it and/or modify it under the terms of the <span class="URL" ><a href=" https://www.fsf.org/licenses/gpl.html " >GNU General Public License</a></span > as published by the Free Software Foundation; either version 3 option ) any later version.</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>span class="URL" ><a href="http://www.tcs.tkk.fi/Software/bliss/ " >bliss</a></span > in <strong class="pkg" >Digraphs</strong >. We also gratefully acknowledge the encouragement and assistance of Leonard Soicher, and the inspiration of his <span class="URL" ><a href="https://gap-packages.github.io/grape" >GRAPE</a></span > package, at many points throughout the development of <strong class="pkg" >Digraphs</strong >. This package's methods for computing digraph homomorphisms are based on work by Max Neunhöffer, and independently Artur Schäfer.</p> "X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X7F202ABA780E595D" >1 <span class="Heading" >strong class="pkg" >Digraphs</strong > packagespan ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X7DFB63A97E67C0A1" >1 .1 <span class="Heading" >Introduction</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84541F61810C741D" >1 .1 -1 <span class="Heading" >Definitions</span ></a>span >div ></div >div >div class="ContChap" ><a href="chap2_mj.html#X817088B27F90D596" >2 <span class="Heading" >Installing <strong class="pkg" >Digraphs</strong ></span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7DA3059C79842BF3" >2 .1 <span class="Heading" >For those in a hurry</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C1F2E6D860DBDEC" >2 .1 -1 <span class="Heading" >Configuration options</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X780AA9D97EBCA95D" >2 .2 <span class="Heading" >Optional package dependencies</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8493C7587FCF6D8B" >2 .2 -1 <span class="Heading" >The Grape package</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X849F6196875A6DF5" >2 .3 <span class="Heading" >Compiling the kernel module</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X857CBE5484CF703A" >2 .4 <span class="Heading" >Rebuilding the documentation</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X870631C38610AC25" >2 .4 -1 DigraphsMakeDoc</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7862D3F37C5BBDEF" >2 .5 <span class="Heading" >Testing your installation</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86AF4DAE80B978DA" >2 .5 -1 DigraphsTestInstall</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7A20088B7C406C4A" >2 .5 -2 DigraphsTestStandard</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7885EF3E785D4298" >2 .5 -3 DigraphsTestExtreme</a></span >div ></div >div >div class="ContChap" ><a href="chap3_mj.html#X7D34861E863A5D93" >3 <span class="Heading" >Creating digraphs</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7D34861E863A5D93" >3 .1 <span class="Heading" >Creating digraphs</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7877ADC77F85E630" >3 .1 -1 IsDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D7EDF83820ED6F5" >3 .1 -2 IsMutableDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CAFAA89804F80BD" >3 .1 -3 IsImmutableDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E749324800B38A5" >3 .1 -4 IsCayleyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80F1B6D28478D8B9" >3 .1 -5 IsDigraphWithAdjacencyFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86E798B779515678" >3 .1 -6 DigraphByOutNeighboursType</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X834843057CE86655" >3 .1 -7 Digraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8023FE387A3AB609" >3 .1 -8 DigraphByAdjacencyMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F37B6768349E269" >3 .1 -9 DigraphByEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B75C1D680757D6F" >3 .1 -10 EdgeOrbitsDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81BC49B57EAADEFB" >3 .1 -11 DigraphByInNeighbours</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7FCADADC7EC28478" >3 .1 -12 CayleyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7BB820C9813F035F" >3 .1 -13 ListNamedDigraphs</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X83608C407CC8836D" >3 .2 <span class="Heading" >Changing representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7FBC4BDB82FBEDD2" >3 .2 -1 AsBinaryRelation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86834E307EACC670" >3 .2 -2 AsDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B335342839E5146" >3 .2 -3 Graph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C4F13E080EC16B0" >3 .2 -4 AsGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C5360B2799943F3" >3 .2 -5 AsTransformation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X85126078848B420A" >3 .3 <span class="Heading" >New digraphs from old</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83D93A8A8251E6F9" >3 .3 -1 DigraphImmutableCopy</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8399F7427B227228" >3 .3 -2 DigraphImmutableCopyIfImmutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83C51DA182CCEA2F" >3 .3 -3 InducedSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CAF093B85A93D2F" >3 .3 -4 ReducedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X829E3EAC7C4B3B1E" >3 .3 -5 MaximalSymmetricSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79BA6A66846D5A95" >3 .3 -6 MaximalAntiSymmetricSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DD9766C86D3ED20" >3 .3 -7 UndirectedSpanningForest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79C770918610AD97" >3 .3 -8 DigraphShortestPathSpanningTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D1D26D27F5B56C2" >3 .3 -9 QuotientDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78DECD26811EFD7C" >3 .3 -10 DigraphReverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F71D99D852B130F" >3 .3 -11 DigraphDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X874883DD7DD450C4" >3 .3 -12 DigraphSymmetricClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A6C419080AD41DE" >3 .3 -13 DigraphTransitiveClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82AD17517E273600" >3 .3 -14 DigraphTransitiveReduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83B2506D79453208" >3 .3 -15 DigraphAddVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8134BEE7786BD3A7" >3 .3 -16 DigraphAddVertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E58CC4880627658" >3 .3 -17 DigraphAddEdge</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7BE5C7028760B053" >3 .3 -18 DigraphAddEdgeOrbit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8693A61B7F752C76" >3 .3 -19 DigraphAddEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B634A2B83C08B16" >3 .3 -20 DigraphRemoveVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E290E847A5A299A" >3 .3 -21 DigraphRemoveVertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8433E3BC7E5EA6BF" >3 .3 -22 DigraphRemoveEdge</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X85981D9187F49018" >3 .3 -23 DigraphRemoveEdgeOrbit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X87093FDA7F88E732" >3 .3 -24 DigraphRemoveEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79324AF7818C0C02" >3 .3 -25 DigraphRemoveLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DCCD0247897A3DE" >3 .3 -26 DigraphRemoveAllMultipleEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X792AD1147E2BFCB7" >3 .3 -27 DigraphContractEdge</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7821753D85402A8C" >3 .3 -28 DigraphReverseEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X814F1DFC83DB273F" >3 .3 -29 DigraphDisjointUnion</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DA997697D310E44" >3 .3 -30 DigraphEdgeUnion</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DDFC759860E3390" >3 .3 -31 DigraphJoin</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D625CC87DBFFDED" >3 .3 -32 DigraphCartesianProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84D24DC9833B54A5" >3 .3 -33 DigraphDirectProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8160BCC378AF000F" >3 .3 -34 ConormalProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79FD2AF279F20A72" >3 .3 -35 HomomorphicProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8151176882BA9901" >3 .3 -36 LexicographicProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X807F95057F9DF576" >3 .3 -37 ModularProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82E200F07FEFAF27" >3 .3 -38 StrongProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8795087A78FE7D54" >3 .3 -39 DigraphCartesianProductProjections</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84FB64F185B804C2" >3 .3 -40 DigraphDirectProductProjections</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8595BF937B749F22" >3 .3 -41 LineDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8364C6F17A1680CB" >3 .3 -42 LineUndirectedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7FB8B48C87C0ED16" >3 .3 -43 DoubleDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C6E6CB284982C7A" >3 .3 -44 BipartiteDoubleDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8167A50A83256ED1" >3 .3 -45 DigraphAddAllLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X865436437DF95FEF" >3 .3 -46 DistanceDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86F9CCEA839ABC48" >3 .3 -47 DigraphClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B5AC5FE859F4D80" >3 .3 -48 DigraphMycielskian</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X85B5D9B97F5187B7" >3 .4 <span class="Heading" >Random digraphs</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86CF9F66788B2A24" >3 .4 -1 RandomDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78FE275E7E77D56F" >3 .4 -2 RandomMultiDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D36B5E57F055051" >3 .4 -3 RandomTournament</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A023E4787682475" >3 .4 -4 RandomLattice</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7C76D1DC7DAF03D3" >3 .5 <span class="Heading" >Standard examples</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D5E3E337D03EDFF" >3 .5 -1 AndrasfaiGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8636C2898395B7DF" >3 .5 -2 BananaTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7FC309427BB170D8" >3 .5 -3 BinaryTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X845C374280D6EAA4" >3 .5 -4 BinomialTreeGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E3240047C92733F" >3 .5 -5 BishopsGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81A0AC37816D287B" >3 .5 -6 BondyGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X861F493382FA7C0B" >3 .5 -7 BookGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8542287E81BDB55E" >3 .5 -8 BurntPancakeGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84C1D3D67E3979A5" >3 .5 -9 PancakeGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B5E9D857D47F5C2" >3 .5 -10 StackedBookGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X870594FC866AC88E" >3 .5 -11 ChainDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DB5AB657A797CF2" >3 .5 -12 CirculantGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X812417E278198D9C" >3 .5 -13 CompleteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8795B0AD856014FA" >3 .5 -14 CompleteBipartiteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X873F29CC863241F8" >3 .5 -15 CompleteMultipartiteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80C29DDE876FFBEB" >3 .5 -16 CycleDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F6EC0AE81531C3C" >3 .5 -17 CycleGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80DAE31A79FEFD40" >3 .5 -18 EmptyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CE45E2B782ADE9A" >3 .5 -19 GearGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X795B62398767E313" >3 .5 -20 HaarGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X801024F57DDC8A39" >3 .5 -21 HalvedCubeGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C43BDE47DF6553A" >3 .5 -22 HanoiGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X782ABFCE812B020A" >3 .5 -23 HelmGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7EE552F88609B1A2" >3 .5 -24 HypercubeGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80ED9CE785819607" >3 .5 -25 JohnsonDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X79483C677AF65688" >3 .5 -26 KellerGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80576A8C861512FD" >3 .5 -27 KingsGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8655BA8584B3ACD0" >3 .5 -28 KneserGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84609DCA79FD9B56" >3 .5 -29 KnightsGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F61140C822880DA" >3 .5 -30 LindgrenSousselierGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X832E82CF87BF5D43" >3 .5 -31 LollipopGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X853613228110588E" >3 .5 -32 MobiusLadderGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X825943547FD7A687" >3 .5 -33 MycielskiGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7904BB2982014ADA" >3 .5 -34 OddGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X815055168405B7F0" >3 .5 -35 PathGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A38DFC47AAE4A96" >3 .5 -36 PermutationStarGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X823F43217A6C375D" >3 .5 -37 PetersenGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B5441F386BD105E" >3 .5 -38 GeneralisedPetersenGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X85425DC5847E6D20" >3 .5 -39 PrismGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X817982877B48D5BD" >3 .5 -40 StackedPrismGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X785C3F1F7D690151" >3 .5 -41 QueensGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A6DD11881874F51" >3 .5 -42 RooksGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8404987F849D7CF2" >3 .5 -43 SquareGridGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8234361278E8816F" >3 .5 -44 TriangularGridGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78F78C077CBAE1EC" >3 .5 -45 StarGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81D59C4D809F4AD3" >3 .5 -46 TadpoleGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7BFA33067F83F8B0" >3 .5 -47 WalshHadamardGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84F3B70A82EEE780" >3 .5 -48 WebGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X817EA60D828A765E" >3 .5 -49 WheelGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7BE44CA27AA5F8DB" >3 .5 -50 WindmillGraph</a></span >div ></div >div >div class="ContChap" ><a href="chap4_mj.html#X7AD6F77E7D95C996" >4 <span class="Heading" >Operators</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X84E0B5B88358C96B" >4 .1 <span class="Heading" >Operators for digraphs</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X829B911D7EFD2D85" >4 .1 -1 IsSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X833C3299787E2309" >4 .1 -2 IsUndirectedSpanningTree</a></span >div ></div >div >div class="ContChap" ><a href="chap5_mj.html#X8739F6CD78C90B14" >5 <span class="Heading" >Attributes and operations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7E814B6478F7D015" >5 .1 <span class="Heading" >Vertices and edges</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C45F7D878D896AC" >5 .1 -1 DigraphVertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C6F19B57CB2E882" >5 .1 -2 DigraphNrVertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D1C6A4D7ECEC317" >5 .1 -3 DigraphEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X85E1CFDD7E164AD0" >5 .1 -4 DigraphNrEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BD5D255809C859E" >5 .1 -5 DigraphNrAdjacencies</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E53E728795BB862" >5 .1 -6 DigraphNrAdjacenciesWithoutLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BDABAF07917462B" >5 .1 -7 DigraphNrLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X85D5E08280914EE4" >5 .1 -8 DigraphSinks</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F5C6268839BE98C" >5 .1 -9 DigraphSources</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X785C30378064CF47" >5 .1 -10 DigraphTopologicalSort</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7CA91E4B7904F793" >5 .1 -11 DigraphVertexLabel</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E51F2FE87140B32" >5 .1 -12 DigraphVertexLabels</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X79FAEACC7F438C2F" >5 .1 -13 DigraphEdgeLabel</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C24851087D4A8FB" >5 .1 -14 DigraphEdgeLabels</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7EFAF01B7A155157" >5 .1 -15 DigraphInEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BECFE6687ECD028" >5 .1 -16 DigraphOutEdges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BB8ED88835F07B4" >5 .1 -17 IsDigraphEdge</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X848FED0B7B4ACD1F" >5 .1 -18 IsMatching</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7B7A67277B1C9A02" >5 .1 -19 DigraphMaximalMatching</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X78E9847A858788D1" >5 .1 -20 DigraphMaximumMatching</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7D7CE8328187D0DF" >5 .2 <span class="Heading" >Neighbours and degree</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DC2CD70830BEE60" >5 .2 -1 AdjacencyMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87FA0A727CDB060B" >5 .2 -2 CharacteristicPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8507DC4F794780C1" >5 .2 -3 BooleanAdjacencyMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7AFCE34A7A04D5C1" >5 .2 -4 DigraphAdjacencyFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FDEBF3279759961" >5 .2 -5 DigraphRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E9880767AE68E00" >5 .2 -6 OutNeighbours</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X85C7AA5A81DA6E11" >5 .2 -7 InNeighbours</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F5ACE807D1BC2E2" >5 .2 -8 OutDegrees</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7ADDFBFD7A365775" >5 .2 -9 InDegrees</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A09EB648070276D" >5 .2 -10 OutDegreeOfVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83315B0186850806" >5 .2 -11 OutNeighboursOfVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C9CD0527CB9E6EF" >5 .2 -12 InDegreeOfVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C0DA18B8291F302" >5 .2 -13 InNeighboursOfVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83271F607BD809CF" >5 .2 -14 DigraphLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BEAE1C78267F54D" >5 .2 -15 DegreeMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X865390B08331936B" >5 .2 -16 LaplacianMatrix</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X86424F167BD4F629" >5 .3 <span class="Heading" >Orders</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DDB33B686B3A2C6" >5 .3 -1 PartialOrderDigraphMeetOfVertices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X824B9896798530F6" >5 .3 -2 NonUpperSemimodularPair</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X8537F4088400DC48" >5 .4 <span class="Heading" >Reachability and connectivity</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F16B9EB8398459C" >5 .4 -1 DigraphDiameter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8104A9D37BCD8A05" >5 .4 -2 DigraphShortestDistance</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X81F99BC67E9D050F" >5 .4 -3 DigraphShortestDistances</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8223718079D98A82" >5 .4 -4 DigraphLongestDistanceFromVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7CB7DDCD84621D38" >5 .4 -5 DigraphDistanceSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X79A3DA4078CF3C90" >5 .4 -6 DigraphGirth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8374B7357EC189C1" >5 .4 -7 DigraphOddGirth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X84688B337BDDBB09" >5 .4 -8 DigraphUndirectedGirth</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X842FAD6A7B835977" >5 .4 -9 DigraphConnectedComponents</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8484EC557810CD31" >5 .4 -10 DigraphConnectedComponent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X833ECD6B7A84944C" >5 .4 -11 DigraphStronglyConnectedComponents</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7EFCB5017D662254" >5 .4 -12 DigraphStronglyConnectedComponent</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F1B5A2782F598B1" >5 .4 -13 DigraphBicomponents</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DDE06E47E605DD7" >5 .4 -14 ArticulationPoints</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X803459AB86AB9BE2" >5 .4 -15 MinimalCyclicEdgeCut</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X84D5A125848BD800" >5 .4 -16 Bridges</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X865590147BD1C507" >5 .4 -17 StrongOrientation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X853D0B0981A33433" >5 .4 -18 DigraphPeriod</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X864A31A8809F61C2" >5 .4 -19 DigraphFloydWarshall</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FBAB09E7C0BE5CF" >5 .4 -20 IsReachable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7ECD22877AEA89CC" >5 .4 -21 IsDigraphPath</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F255A2A84CB868C" >5 .4 -22 VerticesReachableFrom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8039170B82A32257" >5 .4 -23 DigraphPath</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X80E9D645843973A6" >5 .4 -24 DigraphShortestPath</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C45396C808308C4" >5 .4 -25 DigraphRandomWalk</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X787459247B2005E6" >5 .4 -26 DigraphAbsorptionProbabilities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7B0A62CF7F6F23E9" >5 .4 -27 DigraphAbsorptionExpectedSteps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FE79CB278CE6991" >5 .4 -28 Dominators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D66A0FB7F6100FB" >5 .4 -29 DominatorTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C0416FE7A69CA2C" >5 .4 -30 IteratorOfPaths</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7ECD16838704FAAA" >5 .4 -31 DigraphAllSimpleCircuits</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C735C4E86BDD5F6" >5 .4 -32 DigraphLongestSimpleCircuit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F9EDAA8854FB538" >5 .4 -33 DigraphAllUndirectedSimpleCircuits</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F0AC5617CE5E9DD" >5 .4 -34 DigraphAllChordlessCycles</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X805F15398735AD7D" >5 .4 -35 FacialWalks</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X870E04307C5F213F" >5 .4 -36 DigraphLayers</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7B2E42327DA118E0" >5 .4 -37 DigraphDegeneracy</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X827C2BD17A4547E3" >5 .4 -38 DigraphDegeneracyOrdering</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X863FDFC4839A3B82" >5 .4 -39 HamiltonianPath</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X82F30D5681466BC6" >5 .4 -40 NrSpanningTrees</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X79352A8286D1D8F6" >5 .4 -41 DigraphDijkstra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X794CD6037D4CF58C" >5 .4 -42 DigraphCycleBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X835AAF9085BC9D84" >5 .4 -43 DigraphIsKing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A17B9B67AC50561" >5 .4 -44 DigraphKings</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X82F900777D677F55" >5 .5 <span class="Heading" >Cayley graphs of groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A000B1D7CCF7093" >5 .5 -1 GroupOfCayleyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8528455987D7D2BF" >5 .5 -2 GeneratorsOfCayleyDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X790FD6647ECCAE3C" >5 .6 <span class="Heading" >Associated semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87D5C60D7B0C1309" >5 .6 -1 AsSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C6D5EC27C51066B" >5 .6 -2 AsSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7E2305528492DDC0" >5 .7 <span class="Heading" >Planarity</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DC478637E8C190D" >5 .7 -1 KuratowskiPlanarSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X78E8F09A8286501B" >5 .7 -2 KuratowskiOuterPlanarSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X84E3947E7D39BA64" >5 .7 -3 PlanarEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X85DFB8C18088711F" >5 .7 -4 OuterPlanarEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X806D2D6B85E0B269" >5 .7 -5 SubdigraphHomeomorphicToK23</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X876803517C34E1CD" >5 .7 -6 DualPlanarGraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7FF5E2D07D48647E" >5 .8 <span class="Heading" >Hashing</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D97D990867B0149" >5 .8 -1 DigraphHash</a></span >div ></div >div >div class="ContChap" ><a href="chap6_mj.html#X7ADDEFD478D470D5" >6 <span class="Heading" >Properties of digraphs</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7D6A52AB7C69A9CA" >6 .1 <span class="Heading" >Vertex properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X82DBFFF17E708803" >6 .1 -1 DigraphHasAVertex</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78E16B8B7DF55B59" >6 .1 -2 DigraphHasNoVertices</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7F49388F8245F0E9" >6 .2 <span class="Heading" >Edge properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7D92935C7D535187" >6 .2 -1 DigraphHasLoops</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DB1BC2286FC08E2" >6 .2 -2 IsAntiSymmetricDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X860CFB0C8665F356" >6 .2 -3 IsBipartiteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X790A4DBF8533516E" >6 .2 -4 IsCompleteBipartiteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X81F28D4D879FE3B2" >6 .2 -5 IsCompleteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7FD1A15779FEC341" >6 .2 -6 IsCompleteMultipartiteDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E894CCF7B1C27AE" >6 .2 -7 IsEmptyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83762C257DED2751" >6 .2 -8 IsEquivalenceDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E8F37E585DAED52" >6 .2 -9 IsFunctionalDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X793FB02C7C59D85B" >6 .2 -10 IsPermutationDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7BB84CFC7E8B2B26" >6 .2 -11 IsMultiDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E14AE1F7CA23141" >6 .2 -12 IsNonemptyDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8462D8E2792B23F6" >6 .2 -13 IsReflexiveDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X81B3EA7887219860" >6 .2 -14 IsSymmetricDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DD8D1A185EBE865" >6 .2 -15 IsTournament</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7F0835667F29F0C0" >6 .2 -16 IsTransitiveDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X85A9843E80A9B590" >6 .3 <span class="Heading" >Edge Weights</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8639092D8689333D" >6 .3 -1 EdgeWeights</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E14055A84A52A07" >6 .3 -2 EdgeWeightedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X810B2DD7794AFBE8" >6 .3 -3 EdgeWeightedDigraphTotalWeight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E5060AB7FB4F31C" >6 .3 -4 EdgeWeightedDigraphMinimumSpanningTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7EDB9C9A840F6A84" >6 .3 -5 EdgeWeightedDigraphShortestPaths</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DAF81B779BD9165" >6 .3 -6 EdgeWeightedDigraphShortestPath</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X869EFE9F818C6E22" >6 .3 -7 DigraphMaximumFlow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8194E7078167A9E4" >6 .3 -8 RandomUniqueEdgeWeightedDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X86424F167BD4F629" >6 .4 <span class="Heading" >Orders</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8617726C7829F796" >6 .4 -1 IsPreorderDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X82BAE6D37D49A145" >6 .4 -2 IsPartialOrderDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78D3E17B7F737516" >6 .4 -3 IsMeetSemilatticeDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84F4711F7FA36848" >6 .4 -4 DigraphMeetTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X786213437E99065B" >6 .4 -5 IsOrderIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A1D8F4582F8EA53" >6 .4 -6 IsOrderFilter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DEDCD177E5AE824" >6 .4 -7 IsUpperSemimodularDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B566B4A86E18F45" >6 .4 -8 IsDistributiveLatticeDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80659D5784790B52" >6 .4 -9 IsModularLatticeDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7AAF896982EC22FA" >6 .5 <span class="Heading" >Regularity</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A3F78B37E31D9E1" >6 .5 -1 IsInRegularDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7F0A806E7BCB413C" >6 .5 -2 IsOutRegularDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7AF9DB1E7DB12306" >6 .5 -3 IsRegularDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E2082AC7CAE59CD" >6 .5 -4 IsDistanceRegularDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X780DAEB37C5E07FD" >6 .6 <span class="Heading" >Connectivity and cycles</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7BD08D4478218F77" >6 .6 -1 IsAcyclicDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X79563B297C220FB5" >6 .6 -2 IsChainDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83C08C0B7EC1A91F" >6 .6 -3 IsConnectedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X838FAF2D825977BE" >6 .6 -4 IsBiconnectedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7D2A6572820B7F24" >6 .6 -5 IsBridgelessDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B37B9467C68C208" >6 .6 -6 IsStronglyConnectedDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80E883967EBE839E" >6 .6 -7 IsAperiodicDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B46EA6C7B2DF2FB" >6 .6 -8 IsDirectedTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80FC20FA7AC4BC2A" >6 .6 -9 IsUndirectedTree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X79DFBB198525544E" >6 .6 -10 IsEulerianDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X79EFEBC37C2D262D" >6 .6 -11 IsHamiltonianDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E91320B8028F5D8" >6 .6 -12 IsCycleDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7E2305528492DDC0" >6 .7 <span class="Heading" >Planarity</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8606D415858C40AA" >6 .7 -1 IsPlanarDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8251E8B187E7F059" >6 .7 -2 IsOuterPlanarDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X83DC8AD283C41326" >6 .8 <span class="Heading" >Homomorphisms and transformations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78C0B2637985648B" >6 .8 -1 IsDigraphCore</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8361CA6E8401FF26" >6 .8 -2 IsEdgeTransitive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B26E4447A1611E9" >6 .8 -3 IsVertexTransitive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7FB8789A7BF847E6" >6 .8 -4 Is2EdgeTransitive</a></span >div ></div >div >div class="ContChap" ><a href="chap7_mj.html#X84975388859F203D" >7 <span class="Heading" >Homomorphisms</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X8200192B80AD2071" >7 .1 <span class="Heading" >Acting on digraphs</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X808972017C486F1F" >7 .1 -1 OnDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7AFBA7608498F9CE" >7 .1 -2 OnMultiDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F6A97E6870CDDA3" >7 .1 -3 OnTuplesDigraphs</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X7E48B9F87A0F22D4" >7 .2 <span class="Heading" >Isomorphisms and canonical labellings</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X83E593F3855B122E" >7 .2 -1 DigraphsUseNauty</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X858C32127A190175" >7 .2 -2 AutomorphismGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E7B0D88865A89F6" >7 .2 -3 BlissAutomorphismGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X857758B18144C0CD" >7 .2 -4 NautyAutomorphismGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X877732B1783C391B" >7 .2 -5 AutomorphismGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7DA2C4FE837FFE01" >7 .2 -6 AutomorphismGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D676FE67A6684FF" >7 .2 -7 BlissCanonicalLabelling</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87DA265D803DB337" >7 .2 -8 BlissCanonicalLabelling</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X877B1D377EC197D7" >7 .2 -9 BlissCanonicalDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X803ACEDA7BBAC5B3" >7 .2 -10 DigraphGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8096C5287E459279" >7 .2 -11 DigraphOrbits</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8386028782F2D3FF" >7 .2 -12 DigraphOrbitReps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8657604E87A25E5F" >7 .2 -13 DigraphSchreierVector</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X78913684795FB256" >7 .2 -14 DigraphStabilizer</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B4F24B283C9EE28" >7 .2 -15 IsIsomorphicDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D4A1FA8868DA930" >7 .2 -16 IsIsomorphicDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8219FE6C839D9457" >7 .2 -17 IsomorphismDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7ED93C0F86D9D34F" >7 .2 -18 IsomorphismDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E1C806D81DFE15E" >7 .2 -19 RepresentativeOutNeighbours</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X80183D4A7C51365A" >7 .2 -20 IsDigraphIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F16B8B3825A627A" >7 .2 -21 IsDigraphColouring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D4378F27B49C9AC" >7 .2 -22 MaximalCommonSubdigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B99C75B8021FCDA" >7 .2 -23 MinimalCommonSuperdigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X7E1A02FE8384C03C" >7 .3 <span class="Heading" >Homomorphisms of digraphs</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79ABF0E783FD67C7" >7 .3 -1 HomomorphismDigraphsFinder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X85E9B019877AD7FE" >7 .3 -2 DigraphHomomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8653EDA183E06D05" >7 .3 -3 HomomorphismsDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X82D0FCD87D47ACA8" >7 .3 -4 DigraphMonomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X84B4BDB984C2A9A8" >7 .3 -5 MonomorphismsDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7CB5AD9F861684FD" >7 .3 -6 DigraphEpimorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7DFB1F5D873937B3" >7 .3 -7 EpimorphismsDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7AD04CC186E86CCA" >7 .3 -8 DigraphEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X82EBDF137EEDC5FD" >7 .3 -9 EmbeddingsDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X80FE9FCB79718A61" >7 .3 -10 IsDigraphHomomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D6B5A0887903810" >7 .3 -11 IsDigraphEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87E60FB17BC444EF" >7 .3 -12 SubdigraphsMonomorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F80709A80CBFA98" >7 .3 -13 DigraphsRespectsColouring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E93B268823F6478" >7 .3 -14 GeneratorsOfEndomorphismMonoid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X86D0A74B83D6B9A7" >7 .3 -15 DigraphColouring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7AB7200D831013C1" >7 .3 -16 DigraphGreedyColouring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F9CB3B27B9590DB" >7 .3 -17 DigraphWelshPowellOrder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X807D49358529A37C" >7 .3 -18 ChromaticNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X863487EF7D64EF56" >7 .3 -19 DigraphCore</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7EEA340C81FCA52D" >7 .3 -20 LatticeDigraphEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E183D4979D324EF" >7 .3 -21 IsLatticeHomomorphism</a></span >div ></div >div >div class="ContChap" ><a href="chap8_mj.html#X7A7E0B957932DF44" >8 <span class="Heading" >Finding cliques and independent sets</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X788474E38446039B" >8 .1 <span class="Heading" >Finding cliques</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X80670E3E7C36183F" >8 .1 -1 IsClique</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7A3BC9FF8169ABCD" >8 .1 -2 CliquesFinder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X789854AC7B466402" >8 .1 -3 DigraphClique</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X84EA2F9482B8D4AF" >8 .1 -4 DigraphMaximalCliques</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X78427A8B81FEB457" >8 .1 -5 CliqueNumber</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X7E31253287708348" >8 .2 <span class="Heading" >Finding independent sets</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X790733B67B0BC894" >8 .2 -1 IsIndependentSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X84350678782BFAB7" >8 .2 -2 DigraphIndependentSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7D2C78EB81A798A9" >8 .2 -3 DigraphMaximalIndependentSets</a></span >div ></div >div >div class="ContChap" ><a href="chap9_mj.html#X81714DBC80CC4BCB" >9 <span class="Heading" >Visualising and IO</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7CF67F8278D9469C" >9 .1 <span class="Heading" >Visualising a digraph</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X83B3318784E78415" >9 .1 -1 Splash</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F9B99C478EE093A" >9 .1 -2 DotDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X78DA31D1869D2F94" >9 .1 -3 DotSymmetricDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X84120D447E2CAC23" >9 .1 -4 DotPartialOrderDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F5653C8854FAEA6" >9 .1 -5 DotPreorderDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X808D12CF81E2C19F" >9 .1 -6 DotHighlightedDigraph</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X81C9B1DC791C0BBD" >9 .2 <span class="Heading" >Reading and writing digraphs to a file</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X81FB5BE27903EC32" >9 .2 -1 String</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X873D6EB8836A3C61" >9 .2 -2 DigraphFromGraph6String</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X782A052979EA2376" >9 .2 -3 Graph6String</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87DD8B1E867760A5" >9 .2 -4 DigraphFromDreadnautString</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7923733D86767CE1" >9 .2 -5 DIMACSString</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7845ACDA7D4D333D" >9 .2 -6 DigraphFile</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E8142007ED0CB9F" >9 .2 -7 ReadDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X82A4F0767C9EFC87" >9 .2 -8 WriteDigraphs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86D531B287733561" >9 .2 -9 IteratorFromDigraphFile</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7AAA35867B5D8BF4" >9 .2 -10 DigraphPlainTextLineEncoder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7808D99079295C22" >9 .2 -11 TournamentLineDecoder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DF22D1687D096D6" >9 .2 -12 AdjacencyMatrixUpperTriangleLineDecoder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X875393338486D77D" >9 .2 -13 TCodeDecoder</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8540FC21796A793F" >9 .2 -14 PlainTextString</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X81BD23697857B244" >9 .2 -15 WritePlainTextDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X804FDF6A7ED64049" >9 .2 -16 WriteDIMACSDigraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7BC595AF841B78A9" >9 .2 -17 WholeFileEncoders</a></span >div ></div >div >div class="ContChap" ><a href="chapA_mj.html#X800DAF137BA8E25B" >A <span class="Heading" >Command Map span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7CC8A9DB86F9F0F4" >A.1 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7C38A6397D2770FB" >A.2 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X78A5A34783C70CD7" >A.3 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7C74978D85F7AF5C" >A.4 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7E51B92F7E89E266" >A.5 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7A61E3FC7A2BB50E" >A.6 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7DFC61EC7CBDBC7E" >A.7 <span class="Heading" >span ></a>span >div >div >div class="ContChap" ><a href="chapB_mj.html#X819C7A688246B572" >B <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7D4AB14683444D77" >B.1 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7E738C697CA72B1F" >B.2 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7DFB63A97E67C0A1" >B.3 <span class="Heading" >span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X80AD820D85A4C8DA" >B.4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X792906427BCCD4D1" >B.4 -1 <span class="Heading" >Input Filesspan ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7B0FD9A97D715330" >B.4 -2 <span class="Heading" >Output Filesspan ></a>span >div ></div >div >div class="ContChap" ><a href="chapBib_mj.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1 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