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<section id="dag-to-branching">
<h1>dag_to_branching<a class="headerlink" href="#dag-to-branching" title="Permalink to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="networkx.algorithms.dag.dag_to_branching">
<span class="sig-name descname"><span class="pre">dag_to_branching</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">G</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/networkx/algorithms/dag.html#dag_to_branching"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#networkx.algorithms.dag.dag_to_branching" title="Permalink to this definition">#</a></dt>
<dd><p>Returns a branching representing all (overlapping) paths from
root nodes to leaf nodes in the given directed acyclic graph.</p>
<p>As described in <a class="reference internal" href="../tree.html#module-networkx.algorithms.tree.recognition" title="networkx.algorithms.tree.recognition"><code class="xref py py-mod docutils literal notranslate"><span class="pre">networkx.algorithms.tree.recognition</span></code></a>, a
<em>branching</em> is a directed forest in which each node has at most one
parent. In other words, a branching is a disjoint union of
<em>arborescences</em>. For this function, each node of in-degree zero in
<code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> becomes a root of one of the arborescences, and there will be
one leaf node for each distinct path from that root to a leaf node
in <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code>.</p>
<p>Each node <code class="xref py py-obj docutils literal notranslate"><span class="pre">v</span></code> in <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> with <em>k</em> parents becomes <em>k</em> distinct nodes in
the returned branching, one for each parent, and the sub-DAG rooted
at <code class="xref py py-obj docutils literal notranslate"><span class="pre">v</span></code> is duplicated for each copy. The algorithm then recurses on
the children of each copy of <code class="xref py py-obj docutils literal notranslate"><span class="pre">v</span></code>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>G</strong><span class="classifier">NetworkX graph</span></dt><dd><p>A directed acyclic graph.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt>DiGraph</dt><dd><p>The branching in which there is a bijection between root-to-leaf
paths in <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> (in which multiple paths may share the same leaf)
and root-to-leaf paths in the branching (in which there is a
unique path from a root to a leaf).</p>
<p>Each node has an attribute ‘source’ whose value is the original
node to which this node corresponds. No other graph, node, or
edge attributes are copied into this new graph.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>NetworkXNotImplemented</dt><dd><p>If <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> is not directed, or if <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> is a multigraph.</p>
</dd>
<dt>HasACycle</dt><dd><p>If <code class="xref py py-obj docutils literal notranslate"><span class="pre">G</span></code> is not acyclic.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>This function is not idempotent in the sense that the node labels in
the returned branching may be uniquely generated each time the
function is invoked. In fact, the node labels may not be integers;
in order to relabel the nodes to be more readable, you can use the
<code class="xref py py-func docutils literal notranslate"><span class="pre">networkx.convert_node_labels_to_integers()</span></code> function.</p>
<p>The current implementation of this function uses
<code class="xref py py-func docutils literal notranslate"><span class="pre">networkx.prefix_tree()</span></code>, so it is subject to the limitations of
that function.</p>
<p class="rubric">Examples</p>
<p>To examine which nodes in the returned branching were produced by
which original node in the directed acyclic graph, we can collect
the mapping from source node to new nodes into a dictionary. For
example, consider the directed diamond graph:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">operator</span> <span class="kn">import</span> <span class="n">itemgetter</span>
<span class="go">>>></span>
<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">DiGraph</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">pairwise</span><span class="p">(</span><span class="s2">"abd"</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">pairwise</span><span class="p">(</span><span class="s2">"acd"</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">B</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">dag_to_branching</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="go">>>></span>
<span class="gp">>>> </span><span class="n">sources</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">set</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">v</span><span class="p">,</span> <span class="n">source</span> <span class="ow">in</span> <span class="n">B</span><span class="o">.</span><span class="n">nodes</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="s2">"source"</span><span class="p">):</span>
<span class="gp">... </span> <span class="n">sources</span><span class="p">[</span><span class="n">source</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">sources</span><span class="p">[</span><span class="s2">"a"</span><span class="p">])</span>
<span class="go">1</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">sources</span><span class="p">[</span><span class="s2">"d"</span><span class="p">])</span>
<span class="go">2</span>
</pre></div>
</div>
<p>To copy node attributes from the original graph to the new graph,
you can use a dictionary like the one constructed in the above
example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">source</span><span class="p">,</span> <span class="n">nodes</span> <span class="ow">in</span> <span class="n">sources</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">B</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">source</span><span class="p">])</span>
</pre></div>
</div>
</dd></dl>
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