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<div class="section" id="all-simple-paths">
<h1>all_simple_paths<a class="headerlink" href="#all-simple-paths" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="networkx.algorithms.simple_paths.all_simple_paths">
<tt class="descname">all_simple_paths</tt><big>(</big><em>G</em>, <em>source</em>, <em>target</em>, <em>cutoff=None</em><big>)</big><a class="reference internal" href="../../_modules/networkx/algorithms/simple_paths.html#all_simple_paths"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#networkx.algorithms.simple_paths.all_simple_paths" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate all simple paths in the graph G from source to target.</p>
<p>A simple path is a path with no repeated nodes.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>G</strong> : NetworkX graph</p>
<p><strong>source</strong> : node</p>
<blockquote>
<div><p>Starting node for path</p>
</div></blockquote>
<p><strong>target</strong> : node</p>
<blockquote>
<div><p>Ending node for path</p>
</div></blockquote>
<p><strong>cutoff</strong> : integer, optional</p>
<blockquote>
<div><p>Depth to stop the search. Only paths of length <= cutoff are returned.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>path_generator: generator</strong> :</p>
<blockquote class="last">
<div><p>A generator that produces lists of simple paths. If there are no paths
between the source and target within the given cutoff the generator
produces no output.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><tt class="xref py py-obj docutils literal"><span class="pre">all_shortest_paths</span></tt>, <tt class="xref py py-obj docutils literal"><span class="pre">shortest_path</span></tt></p>
</div>
<p class="rubric">Notes</p>
<p>This algorithm uses a modified depth-first search to generate the
paths <a class="reference internal" href="#r245">[R245]</a>. A single path can be found in <span class="math">O(V+E)</span> time but the
number of simple paths in a graph can be very large, e.g. <span class="math">O(n!)</span> in
the complete graph of order n.</p>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="r245" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[R245]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id2">2</a>)</em> R. Sedgewick, “Algorithms in C, Part 5: Graph Algorithms”,
Addison Wesley Professional, 3rd ed., 2001.</td></tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">complete_graph</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">path</span> <span class="ow">in</span> <span class="n">nx</span><span class="o">.</span><span class="n">all_simple_paths</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">print</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
<span class="gp">...</span>
<span class="go">[0, 1, 2, 3]</span>
<span class="go">[0, 1, 3]</span>
<span class="go">[0, 2, 1, 3]</span>
<span class="go">[0, 2, 3]</span>
<span class="go">[0, 3]</span>
<span class="gp">>>> </span><span class="n">paths</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">all_simple_paths</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">paths</span><span class="p">))</span>
<span class="go">[[0, 1, 3], [0, 2, 3], [0, 3]]</span>
</pre></div>
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