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      <h1>newEdges -- replaces disjoint pairs of edges by disjoint pairs of two-chains</h1>
      <ul>
        <li>
          <dl class="element">
            <dt>Usage: </dt>
            <dd><code class="language-macaulay2">N' = newEdges L</code></dd>
            <dd><code class="language-macaulay2">N = newEdges S</code></dd>
            <dd><code class="language-macaulay2">N = newEdges(G, R)</code></dd>
          </dl>
        </li>
        <li>Inputs:          <ul>
            <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, containing graphs in various formats</span></li>
            <li><span><span class="tt">S</span>, <span>a <a title="the class of all strings" href="../../Macaulay2Doc/html/___String.html">string</a></span>, a graph encoded in either Sparse6 or Graph6 format</span></li>
            <li><span><span class="tt">G</span>, <span>a <a title="a class for graphs" href="../../EdgeIdeals/html/___Graph.html">graph</a></span>, </span></li>
            <li><span><span class="tt">R</span>, <span>a <a title="the class of all ordered monoid rings" href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a ring with exactly two more variables than the ring of $G$</span></li>
          </ul>
        </li>
        <li>Outputs:          <ul>
            <li><span><span class="tt">N'</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, containing graphs in either Graph6 or Sparse6 format, modified as described below</span></li>
            <li><span><span class="tt">N</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of graphs, in the same format as the input, modified as described below</span></li>
          </ul>
        </li>
      </ul>
      <div>
        <h2>Description</h2>
        <div>
          <p>The list of &quot;new edge&quot; graphs are formed as follows: Let $ab$ and $cd$ be disjoint edges of $G$.  Then the associated &quot;new edge&quot; graph $H$ is $G$ with the edges $ab$ and $cd$ removed, the vertices $e$ and $f$ added, and the new edges $ae, be, cf, df,$ and $ef$ added.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i1 : R = QQ[a..d];</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : G = graph {a*b, c*d};</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : S = QQ[a..f];</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : newEdges(G, S)

o4 = {Graph{&quot;edges&quot; => {{a, e}, {b, e}, {c, f}, {d, f}, {e, f}}}}
            &quot;ring&quot; => S
            &quot;vertices&quot; => {a, b, c, d, e, f}

o4 : List</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>If the List input format is used, then one should use care as the list may contain isomorphic pairs.</p>
        </div>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">newEdges</span>:</h2>
          <ul>
            <li><kbd>newEdges(Graph,PolynomialRing)</kbd></li>
            <li><kbd>newEdges(List)</kbd></li>
            <li><kbd>newEdges(String)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="replaces disjoint pairs of edges by disjoint pairs of two-chains" href="_new__Edges.html">newEdges</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Nauty.m2:1413:0</span>.</p>
        </div>
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