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<!DOCTYPE html> <html lang="en"> <head> <title>Nauty -- Interface to nauty</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Interface to nauty" href="index.html">Nauty</a> :: <a title="Interface to nauty" href="index.html">Nauty</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_add__Edges.html">next</a> | previous | <a href="_add__Edges.html">forward</a> | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Nauty -- Interface to nauty</h1> <div> <h2>Description</h2> <div> <p>This package provides an interface from Macaulay2 to many of the functions provided in the software nauty by Brendan D. McKay, available at <a href="http://cs.anu.edu.au/~bdm/nauty/">http://cs.anu.edu.au/~bdm/nauty/</a>. The nauty package provides very efficient methods for determining whether given graphs are isomorphic, generating all graphs with particular properties, generating random graphs, and more.</p> <p>Most methods can handle graphs in either the Macaulay2 <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">Graph</a> type as provided by the <a title="A package for working with the edge ideals of (hyper)graphs" href="../../EdgeIdeals/html/index.html">EdgeIdeals</a> package or as Graph6 and Sparse6 strings as used by nauty. The purpose of this is that graphs stored as strings are greatly more efficient than graphs stored as instances of the class <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">Graph</a>. (See <a href="___Comparison_spof_sp__Graph6_spand_sp__Sparse6_spformats.html">Comparison of Graph6 and Sparse6 formats</a>.)</p> <p>It is recommended to work with graphs represented as strings while using nauty-provided methods and then converting the graphs to instances of the class <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">Graph</a> for further work (e.g., computing the chromatic number).</p> <p>The theoretical underpinnings of nauty are in the paper: B. D. McKay, "Practical graph isomorphism," Congr. Numer. 30 (1981), 45–87.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a href="___Comparison_spof_sp__Graph6_spand_sp__Sparse6_spformats.html">Comparison of Graph6 and Sparse6 formats</a></span></li> <li><span><a href="___Example_co_sp__Checking_spfor_spisomorphic_spgraphs.html">Example: Checking for isomorphic graphs</a></span></li> <li><span><a href="___Example_co_sp__Generating_spand_spfiltering_spgraphs.html">Example: Generating and filtering graphs</a></span></li> </ul> </div> <div> <div> <div> <h2>Author</h2> <ul> <li><a href="http://ux1.eiu.edu/~dwcook/">David Cook II</a><span> <<a href="mailto:dwcook%40eiu.edu">dwcook@eiu.edu</a>></span></li> </ul> </div> <div> <h2>Certification <img src="../../../../Macaulay2/Style/GoldStar.png" alt="a gold star"> </h2> <p>Version <b>1.4.1</b> of this package was accepted for publication in <a href="https://msp.org/jsag/2011/3-1/">volume 3</a> of <a href="https://msp.org/jsag/">The Journal of Software for Algebra and Geometry: Macaulay2</a> on 2011-04-20, in the article <a href="https://msp.org/jsag/2011/3-1/p01.xhtml">Nauty in Macaulay2</a> (DOI: <a href="https://doi.org/10.2140/jsag.2011.3.1">10.2140/jsag.2011.3.1</a>). That version can be obtained from <a href="https://msp.org/jsag/2011/3-1/jsag-v3-n1-x01-code.zip">the journal</a>.</p> </div> <div> <h2>Version</h2> <p>This documentation describes version <b>1.4.3.1</b> of Nauty, released <b>01. March 2013</b>.</p> </div> <div> <h2>Citation</h2> <p>If you have used this package in your research, please cite it as follows:</p> <table class="examples"> <tr> <td> <pre><code class="language-bib">@misc{NautySource, title = {{Nauty: interface to nauty. Version~1.4.3.1}}, author = {David Cook II}, howpublished = {A \emph{Macaulay2} package available at \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}} } @article{NautyArticle, title = {{Nauty in \emph{Macaulay2}}}, author = {David Cook II}, journal = {The Journal of Software for Algebra and Geometry: Macaulay2}, volume = {3}, year = {2011}, } </code></pre> </td> </tr> </table> </div> <div> <h2>Exports</h2> <div class="exports"> <ul> <li>Functions and commands <ul> <li><span><a title="creates a list of graphs obtained by adding one new edge to the given graph in all possible ways" href="_add__Edges.html">addEdges</a> -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways</span></li> <li><span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></li> <li><span><a title="creates the appropriate filter string for use with filterGraphs and countGraphs" href="_build__Graph__Filter.html">buildGraphFilter</a> -- creates the appropriate filter string for use with filterGraphs and countGraphs</span></li> <li><span><a title="counts the number of graphs in the list with given properties" href="_count__Graphs.html">countGraphs</a> -- counts the number of graphs in the list with given properties</span></li> <li><span><a title="filters (i.e., selects) graphs in a list for given properties" href="_filter__Graphs.html">filterGraphs</a> -- filters (i.e., selects) graphs in a list for given properties</span></li> <li><span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></li> <li><span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></li> <li><span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></li> <li><span><a title="generates random regular graphs on a given number of vertices" href="_generate__Random__Regular__Graphs.html">generateRandomRegularGraphs</a> -- generates random regular graphs on a given number of vertices</span></li> <li><span><a title="converts a Graph6 string to a Sparse6 string" href="_graph6__To__Sparse6.html">graph6ToSparse6</a> -- converts a Graph6 string to a Sparse6 string</span></li> <li><span><a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a> -- computes the complement of a graph</span></li> <li><span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></li> <li><span><a title="determines if a given graph is planar" href="_is__Planar.html">isPlanar</a> -- determines if a given graph is planar</span></li> <li><span><a title="complements the neighborhood for each vertex, individually" href="_neighborhood__Complements.html">neighborhoodComplements</a> -- complements the neighborhood for each vertex, individually</span></li> <li><span><a title="replaces disjoint pairs of edges by disjoint pairs of two-chains" href="_new__Edges.html">newEdges</a> -- replaces disjoint pairs of edges by disjoint pairs of two-chains</span></li> <li><span><a title="removes non-planar graphs from a list" href="_only__Planar.html">onlyPlanar</a> -- removes non-planar graphs from a list</span></li> <li><span><a title="relabels a bipartite graph so all vertices of a given class are contiguous" href="_relabel__Bipartite.html">relabelBipartite</a> -- relabels a bipartite graph so all vertices of a given class are contiguous</span></li> <li><span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></li> <li><span><a title="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</a> -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</span></li> <li><span><a title="removes all isomorphs from a list of graphs" href="_remove__Isomorphs.html">removeIsomorphs</a> -- removes all isomorphs from a list of graphs</span></li> <li><span><a title="converts a Sparse6 string to a Graph6 string" href="_sparse6__To__Graph6.html">sparse6ToGraph6</a> -- converts a Sparse6 string to a Graph6 string</span></li> <li><span><a title="converts a Sparse6 or Graph6 String to an edge ideal in the given polynomial ring" href="_string__To__Edge__Ideal.html">stringToEdgeIdeal</a> -- converts a Sparse6 or Graph6 String to an edge ideal in the given polynomial ring</span></li> <li><span><a title="converts a Sparse6 or Graph6 String to a Graph in the given polynomial ring" href="_string__To__Graph.html">stringToGraph</a> -- converts a Sparse6 or Graph6 String to a Graph in the given polynomial ring</span></li> </ul> </li> <li>Methods <ul> <li><span><kbd>addEdges(Graph)</kbd> -- see <span><a title="creates a list of graphs obtained by adding one new edge to the given graph in all possible ways" href="_add__Edges.html">addEdges</a> -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways</span></span></li> <li><span><kbd>addEdges(List)</kbd> -- see <span><a title="creates a list of graphs obtained by adding one new edge to the given graph in all possible ways" href="_add__Edges.html">addEdges</a> -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways</span></span></li> <li><span><kbd>addEdges(String)</kbd> -- see <span><a title="creates a list of graphs obtained by adding one new edge to the given graph in all possible ways" href="_add__Edges.html">addEdges</a> -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways</span></span></li> <li><span><kbd>areIsomorphic(Graph,Graph)</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>areIsomorphic(Graph,String)</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>areIsomorphic(String,Graph)</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>areIsomorphic(String,String)</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>Graph == Graph</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>Graph == String</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>String == Graph</kbd> -- see <span><a title="determines whether two graphs are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines whether two graphs are isomorphic</span></span></li> <li><span><kbd>buildGraphFilter(HashTable)</kbd> -- see <span><a title="creates the appropriate filter string for use with filterGraphs and countGraphs" href="_build__Graph__Filter.html">buildGraphFilter</a> -- creates the appropriate filter string for use with filterGraphs and countGraphs</span></span></li> <li><span><kbd>buildGraphFilter(List)</kbd> -- see <span><a title="creates the appropriate filter string for use with filterGraphs and countGraphs" href="_build__Graph__Filter.html">buildGraphFilter</a> -- creates the appropriate filter string for use with filterGraphs and countGraphs</span></span></li> <li><span><kbd>countGraphs(List,HashTable)</kbd> -- see <span><a title="counts the number of graphs in the list with given properties" href="_count__Graphs.html">countGraphs</a> -- counts the number of graphs in the list with given properties</span></span></li> <li><span><kbd>countGraphs(List,List)</kbd> -- see <span><a title="counts the number of graphs in the list with given properties" href="_count__Graphs.html">countGraphs</a> -- counts the number of graphs in the list with given properties</span></span></li> <li><span><kbd>countGraphs(List,String)</kbd> -- see <span><a title="counts the number of graphs in the list with given properties" href="_count__Graphs.html">countGraphs</a> -- counts the number of graphs in the list with given properties</span></span></li> <li><span><kbd>filterGraphs(List,HashTable)</kbd> -- see <span><a title="filters (i.e., selects) graphs in a list for given properties" href="_filter__Graphs.html">filterGraphs</a> -- filters (i.e., selects) graphs in a list for given properties</span></span></li> <li><span><kbd>filterGraphs(List,List)</kbd> -- see <span><a title="filters (i.e., selects) graphs in a list for given properties" href="_filter__Graphs.html">filterGraphs</a> -- filters (i.e., selects) graphs in a list for given properties</span></span></li> <li><span><kbd>filterGraphs(List,String)</kbd> -- see <span><a title="filters (i.e., selects) graphs in a list for given properties" href="_filter__Graphs.html">filterGraphs</a> -- filters (i.e., selects) graphs in a list for given properties</span></span></li> <li><span><kbd>generateBipartiteGraphs(PolynomialRing)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(PolynomialRing,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(PolynomialRing,ZZ,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(PolynomialRing,ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(ZZ,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateBipartiteGraphs(ZZ,ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates the bipartite graphs with a given bipartition" href="_generate__Bipartite__Graphs.html">generateBipartiteGraphs</a> -- generates the bipartite graphs with a given bipartition</span></span></li> <li><span><kbd>generateGraphs(PolynomialRing)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateGraphs(PolynomialRing,ZZ)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateGraphs(PolynomialRing,ZZ,ZZ)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateGraphs(ZZ)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateGraphs(ZZ,ZZ)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateGraphs(ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates the graphs on a given number of vertices" href="_generate__Graphs.html">generateGraphs</a> -- generates the graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(PolynomialRing,ZZ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(PolynomialRing,ZZ,QQ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(PolynomialRing,ZZ,RR)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(PolynomialRing,ZZ,ZZ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(ZZ,ZZ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(ZZ,ZZ,QQ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(ZZ,ZZ,RR)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomGraphs(ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates random graphs on a given number of vertices" href="_generate__Random__Graphs.html">generateRandomGraphs</a> -- generates random graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomRegularGraphs(PolynomialRing,ZZ,ZZ)</kbd> -- see <span><a title="generates random regular graphs on a given number of vertices" href="_generate__Random__Regular__Graphs.html">generateRandomRegularGraphs</a> -- generates random regular graphs on a given number of vertices</span></span></li> <li><span><kbd>generateRandomRegularGraphs(ZZ,ZZ,ZZ)</kbd> -- see <span><a title="generates random regular graphs on a given number of vertices" href="_generate__Random__Regular__Graphs.html">generateRandomRegularGraphs</a> -- generates random regular graphs on a given number of vertices</span></span></li> <li><span><kbd>graph6ToSparse6(String)</kbd> -- see <span><a title="converts a Graph6 string to a Sparse6 string" href="_graph6__To__Sparse6.html">graph6ToSparse6</a> -- converts a Graph6 string to a Sparse6 string</span></span></li> <li><span><kbd>graphComplement(Graph)</kbd> -- see <span><a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a> -- computes the complement of a graph</span></span></li> <li><span><kbd>graphComplement(List)</kbd> -- see <span><a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a> -- computes the complement of a graph</span></span></li> <li><span><kbd>graphComplement(String)</kbd> -- see <span><a title="computes the complement of a graph" href="_graph__Complement.html">graphComplement</a> -- computes the complement of a graph</span></span></li> <li><span><kbd>graphToString(Graph)</kbd> -- see <span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></span></li> <li><span><kbd>graphToString(Ideal)</kbd> -- see <span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></span></li> <li><span><kbd>graphToString(List,ZZ)</kbd> -- see <span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></span></li> <li><span><kbd>graphToString(MonomialIdeal)</kbd> -- see <span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></span></li> <li><span><kbd>graphToString(String)</kbd> -- see <span><a title="converts a graph to a string in the Graph6 format" href="_graph__To__String.html">graphToString</a> -- converts a graph to a string in the Graph6 format</span></span></li> <li><span><kbd>isPlanar(Graph)</kbd> -- see <span><a title="determines if a given graph is planar" href="_is__Planar.html">isPlanar</a> -- determines if a given graph is planar</span></span></li> <li><span><kbd>isPlanar(String)</kbd> -- see <span><a title="determines if a given graph is planar" href="_is__Planar.html">isPlanar</a> -- determines if a given graph is planar</span></span></li> <li><span><kbd>neighborhoodComplements(Graph)</kbd> -- see <span><a title="complements the neighborhood for each vertex, individually" href="_neighborhood__Complements.html">neighborhoodComplements</a> -- complements the neighborhood for each vertex, individually</span></span></li> <li><span><kbd>neighborhoodComplements(List)</kbd> -- see <span><a title="complements the neighborhood for each vertex, individually" href="_neighborhood__Complements.html">neighborhoodComplements</a> -- complements the neighborhood for each vertex, individually</span></span></li> <li><span><kbd>neighborhoodComplements(String)</kbd> -- see <span><a title="complements the neighborhood for each vertex, individually" href="_neighborhood__Complements.html">neighborhoodComplements</a> -- complements the neighborhood for each vertex, individually</span></span></li> <li><span><kbd>newEdges(Graph,PolynomialRing)</kbd> -- see <span><a title="replaces disjoint pairs of edges by disjoint pairs of two-chains" href="_new__Edges.html">newEdges</a> -- replaces disjoint pairs of edges by disjoint pairs of two-chains</span></span></li> <li><span><kbd>newEdges(List)</kbd> -- see <span><a title="replaces disjoint pairs of edges by disjoint pairs of two-chains" href="_new__Edges.html">newEdges</a> -- replaces disjoint pairs of edges by disjoint pairs of two-chains</span></span></li> <li><span><kbd>newEdges(String)</kbd> -- see <span><a title="replaces disjoint pairs of edges by disjoint pairs of two-chains" href="_new__Edges.html">newEdges</a> -- replaces disjoint pairs of edges by disjoint pairs of two-chains</span></span></li> <li><span><kbd>onlyPlanar(List)</kbd> -- see <span><a title="removes non-planar graphs from a list" href="_only__Planar.html">onlyPlanar</a> -- removes non-planar graphs from a list</span></span></li> <li><span><kbd>onlyPlanar(List,Boolean)</kbd> -- see <span><a title="removes non-planar graphs from a list" href="_only__Planar.html">onlyPlanar</a> -- removes non-planar graphs from a list</span></span></li> <li><span><kbd>relabelBipartite(Graph)</kbd> -- see <span><a title="relabels a bipartite graph so all vertices of a given class are contiguous" href="_relabel__Bipartite.html">relabelBipartite</a> -- relabels a bipartite graph so all vertices of a given class are contiguous</span></span></li> <li><span><kbd>relabelBipartite(List)</kbd> -- see <span><a title="relabels a bipartite graph so all vertices of a given class are contiguous" href="_relabel__Bipartite.html">relabelBipartite</a> -- relabels a bipartite graph so all vertices of a given class are contiguous</span></span></li> <li><span><kbd>relabelBipartite(String)</kbd> -- see <span><a title="relabels a bipartite graph so all vertices of a given class are contiguous" href="_relabel__Bipartite.html">relabelBipartite</a> -- relabels a bipartite graph so all vertices of a given class are contiguous</span></span></li> <li><span><kbd>relabelGraph(Graph)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(Graph,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(Graph,ZZ,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(List)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(List,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(List,ZZ,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(String)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(String,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>relabelGraph(String,ZZ,ZZ)</kbd> -- see <span><a title="applies a vertex invariant based refinement to a graph" href="_relabel__Graph.html">relabelGraph</a> -- applies a vertex invariant based refinement to a graph</span></span></li> <li><span><kbd>removeEdges(Graph)</kbd> -- see <span><a title="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</a> -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</span></span></li> <li><span><kbd>removeEdges(List)</kbd> -- see <span><a title="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</a> -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</span></span></li> <li><span><kbd>removeEdges(String)</kbd> -- see <span><a title="creates a list of graphs obtained by removing one edge from the given graph in all possible ways" href="_remove__Edges.html">removeEdges</a> -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways</span></span></li> <li><span><kbd>removeIsomorphs(List)</kbd> -- see <span><a title="removes all isomorphs from a list of graphs" href="_remove__Isomorphs.html">removeIsomorphs</a> -- removes all isomorphs from a list of graphs</span></span></li> <li><span><kbd>sparse6ToGraph6(String)</kbd> -- see <span><a title="converts a Sparse6 string to a Graph6 string" href="_sparse6__To__Graph6.html">sparse6ToGraph6</a> -- converts a Sparse6 string to a Graph6 string</span></span></li> <li><span><kbd>stringToEdgeIdeal(String,PolynomialRing)</kbd> -- see <span><a title="converts a Sparse6 or Graph6 String to an edge ideal in the given polynomial ring" href="_string__To__Edge__Ideal.html">stringToEdgeIdeal</a> -- converts a Sparse6 or Graph6 String to an edge ideal in the given polynomial ring</span></span></li> <li><span><kbd>stringToGraph(String,PolynomialRing)</kbd> -- see <span><a title="converts a Sparse6 or Graph6 String to a Graph in the given polynomial ring" href="_string__To__Graph.html">stringToGraph</a> -- converts a Sparse6 or Graph6 String to a Graph in the given polynomial ring</span></span></li> </ul> </li> <li>Symbols</li> </ul> </div> </div> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="Interface to nauty" href="index.html">Nauty</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">Nauty.m2</span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Nauty.m2:540:0</span>.</p> </div> </div> </div> </body> </html>