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Edit File: _top__Sort.html

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    <title>topSort -- topologically sort the vertices of a digraph</title>
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o1 = Digraph{0 => {}    }
             1 => {}
             2 => {3}
             3 => {1}
             4 => {0, 1}
             5 => {2, 0}

o1 : Digraph</code></pre>
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              <pre><code class="language-macaulay2">i2 : H = topSort G

o2 = SortedDigraph{digraph => Digraph{0 => {}    }   }
                                      1 => {}
                                      2 => {3}
                                      3 => {1}
                                      4 => {0, 1}
                                      5 => {2, 0}
                   map => HashTable{0 => 4}
                                    1 => 6
                                    2 => 3
                                    3 => 5
                                    4 => 2
                                    5 => 1
                   newDigraph => Digraph{1 => {3, 4}}
                                         2 => {4, 6}
                                         3 => {5}
                                         4 => {}
                                         5 => {6}
                                         6 => {}

o2 : SortedDigraph</code></pre>
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              <pre><code class="language-macaulay2">i3 : H#digraph

o3 = Digraph{0 => {}    }
             1 => {}
             2 => {3}
             3 => {1}
             4 => {0, 1}
             5 => {2, 0}

o3 : Digraph</code></pre>
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              <pre><code class="language-macaulay2">i4 : H#map

o4 = HashTable{0 => 4}
               1 => 6
               2 => 3
               3 => 5
               4 => 2
               5 => 1

o4 : HashTable</code></pre>
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              <pre><code class="language-macaulay2">i5 : topSort(G,&quot;min&quot;)

o5 = SortedDigraph{digraph => Digraph{0 => {}    }   }
                                      1 => {}
                                      2 => {3}
                                      3 => {1}
                                      4 => {0, 1}
                                      5 => {2, 0}
                   map => HashTable{0 => 3}
                                    1 => 6
                                    2 => 4
                                    3 => 5
                                    4 => 1
                                    5 => 2
                   newDigraph => Digraph{1 => {3, 6}}
                                         2 => {3, 4}
                                         3 => {}
                                         4 => {5}
                                         5 => {6}
                                         6 => {}

o5 : SortedDigraph</code></pre>
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              <pre><code class="language-macaulay2">i6 : topSort(G,&quot;max&quot;)

o6 = SortedDigraph{digraph => Digraph{0 => {}    }   }
                                      1 => {}
                                      2 => {3}
                                      3 => {1}
                                      4 => {0, 1}
                                      5 => {2, 0}
                   map => HashTable{0 => 6}
                                    1 => 5
                                    2 => 3
                                    3 => 4
                                    4 => 2
                                    5 => 1
                   newDigraph => Digraph{1 => {3, 6}}
                                         2 => {5, 6}
                                         3 => {4}
                                         4 => {5}
                                         5 => {}
                                         6 => {}

o6 : SortedDigraph</code></pre>
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              <pre><code class="language-macaulay2">i7 : topSort(G,&quot;random&quot;)

o7 = SortedDigraph{digraph => Digraph{0 => {}    }   }
                                      1 => {}
                                      2 => {3}
                                      3 => {1}
                                      4 => {0, 1}
                                      5 => {2, 0}
                   map => HashTable{0 => 5}
                                    1 => 6
                                    2 => 2
                                    3 => 4
                                    4 => 3
                                    5 => 1
                   newDigraph => Digraph{1 => {2, 5}}
                                         2 => {4}
                                         3 => {5, 6}
                                         4 => {6}
                                         5 => {}
                                         6 => {}

o7 : SortedDigraph</code></pre>
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              <pre><code class="language-macaulay2">i8 : topSort(G,&quot;degree&quot;)

o8 = SortedDigraph{digraph => Digraph{0 => {}    }   }
                                      1 => {}
                                      2 => {3}
                                      3 => {1}
                                      4 => {0, 1}
                                      5 => {2, 0}
                   map => HashTable{0 => 3}
                                    1 => 6
                                    2 => 4
                                    3 => 5
                                    4 => 1
                                    5 => 2
                   newDigraph => Digraph{1 => {3, 6}}
                                         2 => {3, 4}
                                         3 => {}
                                         4 => {5}
                                         5 => {6}
                                         6 => {}

o8 : SortedDigraph</code></pre>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="outputs a list of vertices in a topologically sorted order of a DAG." href="_topological__Sort.html">topologicalSort</a> -- outputs a list of vertices in a topologically sorted order of a DAG.</span></li>
          <li><span><a title="hashtable used in topSort" href="___Sorted__Digraph.html">SortedDigraph</a> -- hashtable used in topSort</span></li>
          <li><span><a title="key used in the output of topSort" href="_new__Digraph.html">newDigraph</a> -- key used in the output of topSort</span></li>
        </ul>
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        <div class="waystouse">
          <h2>Ways to use <span class="tt">topSort</span>:</h2>
          <ul>
            <li><kbd>topSort(Digraph)</kbd></li>
            <li><kbd>topSort(Digraph,String)</kbd></li>
          </ul>
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        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="topologically sort the vertices of a digraph" href="_top__Sort.html">topSort</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p>
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        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Graphs.m2:5336:0</span>.</p>
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