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<section id="digraph-directed-graphs-with-self-loops">
<span id="digraph"></span><h1>DiGraph—Directed graphs with self loops<a class="headerlink" href="#digraph-directed-graphs-with-self-loops" title="Permalink to this heading">#</a></h1>
<section id="overview">
<h2>Overview<a class="headerlink" href="#overview" title="Permalink to this heading">#</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="networkx.DiGraph">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DiGraph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">incoming_graph_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/networkx/classes/digraph.html#DiGraph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#networkx.DiGraph" title="Permalink to this definition">#</a></dt>
<dd><p>Base class for directed graphs.</p>
<p>A DiGraph stores nodes and edges with optional data, or attributes.</p>
<p>DiGraphs hold directed edges. Self loops are allowed but multiple
(parallel) edges are not.</p>
<p>Nodes can be arbitrary (hashable) Python objects with optional
key/value attributes. By convention <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a> is not used as a node.</p>
<p>Edges are represented as links between nodes with optional
key/value attributes.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>incoming_graph_data</strong><span class="classifier">input graph (optional, default: None)</span></dt><dd><p>Data to initialize graph. If None (default) an empty
graph is created. The data can be any format that is supported
by the to_networkx_graph() function, currently including edge list,
dict of dicts, dict of lists, NetworkX graph, 2D NumPy array, SciPy
sparse matrix, or PyGraphviz graph.</p>
</dd>
<dt><strong>attr</strong><span class="classifier">keyword arguments, optional (default= no attributes)</span></dt><dd><p>Attributes to add to graph as key=value pairs.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="graph.html#networkx.Graph" title="networkx.Graph"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Graph</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="multigraph.html#networkx.MultiGraph" title="networkx.MultiGraph"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MultiGraph</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="multidigraph.html#networkx.MultiDiGraph" title="networkx.MultiDiGraph"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MultiDiGraph</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Examples</p>
<p>Create an empty graph structure (a “null graph”) with no nodes and
no edges.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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>
</pre></div>
</div>
<p>G can be grown in several ways.</p>
<p><strong>Nodes:</strong></p>
<p>Add one node at a time:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<p>Add the nodes from any container (a list, dict, set or
even the lines from a file or the nodes from another graph).</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">110</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">H</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
</pre></div>
</div>
<p>In addition to strings and integers any hashable Python object
(except None) can represent a node, e.g. a customized node object,
or even another Graph.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>Edges:</strong></p>
<p>G can also be grown by adding edges.</p>
<p>Add one edge,</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<p>a list of edges,</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)])</span>
</pre></div>
</div>
<p>or a collection of edges,</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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">H</span><span class="o">.</span><span class="n">edges</span><span class="p">)</span>
</pre></div>
</div>
<p>If some edges connect nodes not yet in the graph, the nodes
are added automatically. There are no errors when adding
nodes or edges that already exist.</p>
<p><strong>Attributes:</strong></p>
<p>Each graph, node, and edge can hold key/value attribute pairs
in an associated attribute dictionary (the keys must be hashable).
By default these are empty, but can be added or changed using
add_edge, add_node or direct manipulation of the attribute
dictionaries named graph, node and edge respectively.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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">day</span><span class="o">=</span><span class="s2">"Friday"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">graph</span>
<span class="go">{'day': 'Friday'}</span>
</pre></div>
</div>
<p>Add node attributes using add_node(), add_nodes_from() or G.nodes</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">time</span><span class="o">=</span><span class="s2">"5pm"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">([</span><span class="mi">3</span><span class="p">],</span> <span class="n">time</span><span class="o">=</span><span class="s2">"2pm"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="go">{'time': '5pm'}</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="s2">"room"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">714</span>
<span class="gp">>>> </span><span class="k">del</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="s2">"room"</span><span class="p">]</span> <span class="c1"># remove attribute</span>
<span class="gp">>>> </span><span class="nb">list</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">data</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
<span class="go">[(1, {'time': '5pm'}), (3, {'time': '2pm'})]</span>
</pre></div>
</div>
<p>Add edge attributes using add_edge(), add_edges_from(), subscript
notation, or G.edges.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="mf">4.7</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="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"red"</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="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">{</span><span class="s2">"color"</span><span class="p">:</span> <span class="s2">"blue"</span><span class="p">}),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">{</span><span class="s2">"weight"</span><span class="p">:</span> <span class="mi">8</span><span class="p">})])</span>
<span class="gp">>>> </span><span class="n">G</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">][</span><span class="s2">"weight"</span><span class="p">]</span> <span class="o">=</span> <span class="mf">4.7</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">][</span><span class="s2">"weight"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">4</span>
</pre></div>
</div>
<p>Warning: we protect the graph data structure by making <code class="xref py py-obj docutils literal notranslate"><span class="pre">G.edges[1,</span> <span class="pre">2]</span></code> a
read-only dict-like structure. However, you can assign to attributes
in e.g. <code class="xref py py-obj docutils literal notranslate"><span class="pre">G.edges[1,</span> <span class="pre">2]</span></code>. Thus, use 2 sets of brackets to add/change
data attributes: <code class="xref py py-obj docutils literal notranslate"><span class="pre">G.edges[1,</span> <span class="pre">2]['weight']</span> <span class="pre">=</span> <span class="pre">4</span></code>
(For multigraphs: <code class="xref py py-obj docutils literal notranslate"><span class="pre">MG.edges[u,</span> <span class="pre">v,</span> <span class="pre">key][name]</span> <span class="pre">=</span> <span class="pre">value</span></code>).</p>
<p><strong>Shortcuts:</strong></p>
<p>Many common graph features allow python syntax to speed reporting.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="mi">1</span> <span class="ow">in</span> <span class="n">G</span> <span class="c1"># check if node in graph</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span> <span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">3</span><span class="p">]</span> <span class="c1"># iterate through nodes</span>
<span class="go">[1, 2]</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="c1"># number of nodes in graph</span>
<span class="go">5</span>
</pre></div>
</div>
<p>Often the best way to traverse all edges of a graph is via the neighbors.
The neighbors are reported as an adjacency-dict <code class="xref py py-obj docutils literal notranslate"><span class="pre">G.adj</span></code> or <code class="xref py py-obj docutils literal notranslate"><span class="pre">G.adjacency()</span></code></p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">nbrsdict</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adjacency</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">for</span> <span class="n">nbr</span><span class="p">,</span> <span class="n">eattr</span> <span class="ow">in</span> <span class="n">nbrsdict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">if</span> <span class="s2">"weight"</span> <span class="ow">in</span> <span class="n">eattr</span><span class="p">:</span>
<span class="gp">... </span> <span class="c1"># Do something useful with the edges</span>
<span class="gp">... </span> <span class="k">pass</span>
</pre></div>
</div>
<p>But the edges reporting object is often more convenient:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">weight</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">if</span> <span class="n">weight</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="gp">... </span> <span class="c1"># Do something useful with the edges</span>
<span class="gp">... </span> <span class="k">pass</span>
</pre></div>
</div>
<p><strong>Reporting:</strong></p>
<p>Simple graph information is obtained using object-attributes and methods.
Reporting usually provides views instead of containers to reduce memory
usage. The views update as the graph is updated similarly to dict-views.
The objects <a class="reference internal" href="generated/networkx.DiGraph.nodes.html#networkx.DiGraph.nodes" title="networkx.DiGraph.nodes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes</span></code></a>, <a class="reference internal" href="generated/networkx.DiGraph.edges.html#networkx.DiGraph.edges" title="networkx.DiGraph.edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">edges</span></code></a> and <a class="reference internal" href="generated/networkx.DiGraph.adj.html#networkx.DiGraph.adj" title="networkx.DiGraph.adj"><code class="xref py py-obj docutils literal notranslate"><span class="pre">adj</span></code></a> provide access to data attributes
via lookup (e.g. <code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes[n]</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">edges[u,</span> <span class="pre">v]</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">adj[u][v]</span></code>) and iteration
(e.g. <code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes.items()</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes.data('color')</span></code>,
<code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes.data('color',</span> <span class="pre">default='blue')</span></code> and similarly for <a class="reference internal" href="generated/networkx.DiGraph.edges.html#networkx.DiGraph.edges" title="networkx.DiGraph.edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">edges</span></code></a>)
Views exist for <a class="reference internal" href="generated/networkx.DiGraph.nodes.html#networkx.DiGraph.nodes" title="networkx.DiGraph.nodes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes</span></code></a>, <a class="reference internal" href="generated/networkx.DiGraph.edges.html#networkx.DiGraph.edges" title="networkx.DiGraph.edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">edges</span></code></a>, <a class="reference internal" href="generated/networkx.DiGraph.neighbors.html#networkx.DiGraph.neighbors" title="networkx.DiGraph.neighbors"><code class="xref py py-obj docutils literal notranslate"><span class="pre">neighbors()</span></code></a>/<a class="reference internal" href="generated/networkx.DiGraph.adj.html#networkx.DiGraph.adj" title="networkx.DiGraph.adj"><code class="xref py py-obj docutils literal notranslate"><span class="pre">adj</span></code></a> and <a class="reference internal" href="generated/networkx.DiGraph.degree.html#networkx.DiGraph.degree" title="networkx.DiGraph.degree"><code class="xref py py-obj docutils literal notranslate"><span class="pre">degree</span></code></a>.</p>
<p>For details on these and other miscellaneous methods, see below.</p>
<p><strong>Subclasses (Advanced):</strong></p>
<p>The Graph class uses a dict-of-dict-of-dict data structure.
The outer dict (node_dict) holds adjacency information keyed by node.
The next dict (adjlist_dict) represents the adjacency information and holds
edge data keyed by neighbor. The inner dict (edge_attr_dict) represents
the edge data and holds edge attribute values keyed by attribute names.</p>
<p>Each of these three dicts can be replaced in a subclass by a user defined
dict-like object. In general, the dict-like features should be
maintained but extra features can be added. To replace one of the
dicts create a new graph class by changing the class(!) variable
holding the factory for that dict-like structure. The variable names are
node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory,
adjlist_outer_dict_factory, edge_attr_dict_factory and graph_attr_dict_factory.</p>
<dl class="simple">
<dt>node_dict_factory<span class="classifier">function, (default: dict)</span></dt><dd><p>Factory function to be used to create the dict containing node
attributes, keyed by node id.
It should require no arguments and return a dict-like object</p>
</dd>
<dt>node_attr_dict_factory: function, (default: dict)</dt><dd><p>Factory function to be used to create the node attribute
dict which holds attribute values keyed by attribute name.
It should require no arguments and return a dict-like object</p>
</dd>
<dt>adjlist_outer_dict_factory<span class="classifier">function, (default: dict)</span></dt><dd><p>Factory function to be used to create the outer-most dict
in the data structure that holds adjacency info keyed by node.
It should require no arguments and return a dict-like object.</p>
</dd>
<dt>adjlist_inner_dict_factory<span class="classifier">function, optional (default: dict)</span></dt><dd><p>Factory function to be used to create the adjacency list
dict which holds edge data keyed by neighbor.
It should require no arguments and return a dict-like object</p>
</dd>
<dt>edge_attr_dict_factory<span class="classifier">function, optional (default: dict)</span></dt><dd><p>Factory function to be used to create the edge attribute
dict which holds attribute values keyed by attribute name.
It should require no arguments and return a dict-like object.</p>
</dd>
<dt>graph_attr_dict_factory<span class="classifier">function, (default: dict)</span></dt><dd><p>Factory function to be used to create the graph attribute
dict which holds attribute values keyed by attribute name.
It should require no arguments and return a dict-like object.</p>
</dd>
</dl>
<p>Typically, if your extension doesn’t impact the data structure all
methods will inherited without issue except: <code class="xref py py-obj docutils literal notranslate"><span class="pre">to_directed/to_undirected</span></code>.
By default these methods create a DiGraph/Graph class and you probably
want them to create your extension of a DiGraph/Graph. To facilitate
this we define two class variables that you can set in your subclass.</p>
<dl class="simple">
<dt>to_directed_class<span class="classifier">callable, (default: DiGraph or MultiDiGraph)</span></dt><dd><p>Class to create a new graph structure in the <a class="reference internal" href="generated/networkx.DiGraph.to_directed.html#networkx.DiGraph.to_directed" title="networkx.DiGraph.to_directed"><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_directed</span></code></a> method.
If <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, a NetworkX class (DiGraph or MultiDiGraph) is used.</p>
</dd>
<dt>to_undirected_class<span class="classifier">callable, (default: Graph or MultiGraph)</span></dt><dd><p>Class to create a new graph structure in the <a class="reference internal" href="generated/networkx.DiGraph.to_undirected.html#networkx.DiGraph.to_undirected" title="networkx.DiGraph.to_undirected"><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_undirected</span></code></a> method.
If <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, a NetworkX class (Graph or MultiGraph) is used.</p>
</dd>
</dl>
<p><strong>Subclassing Example</strong></p>
<p>Create a low memory graph class that effectively disallows edge
attributes by using a single attribute dict for all edges.
This reduces the memory used, but you lose edge attributes.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">class</span> <span class="nc">ThinGraph</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">):</span>
<span class="gp">... </span> <span class="n">all_edge_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"weight"</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
<span class="gp">...</span>
<span class="gp">... </span> <span class="k">def</span> <span class="nf">single_edge_dict</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">all_edge_dict</span>
<span class="gp">...</span>
<span class="gp">... </span> <span class="n">edge_attr_dict_factory</span> <span class="o">=</span> <span class="n">single_edge_dict</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">ThinGraph</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
<span class="go">{'weight': 1}</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="n">G</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
</section>
<section id="methods">
<h2>Methods<a class="headerlink" href="#methods" title="Permalink to this heading">#</a></h2>
<section id="adding-and-removing-nodes-and-edges">
<h3>Adding and removing nodes and edges<a class="headerlink" href="#adding-and-removing-nodes-and-edges" title="Permalink to this heading">#</a></h3>
<table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.__init__.html#networkx.DiGraph.__init__" title="networkx.DiGraph.__init__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.__init__</span></code></a>([incoming_graph_data])</p></td>
<td><p>Initialize a graph with edges, name, or graph attributes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.add_node.html#networkx.DiGraph.add_node" title="networkx.DiGraph.add_node"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.add_node</span></code></a>(node_for_adding, **attr)</p></td>
<td><p>Add a single node <code class="xref py py-obj docutils literal notranslate"><span class="pre">node_for_adding</span></code> and update node attributes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.add_nodes_from.html#networkx.DiGraph.add_nodes_from" title="networkx.DiGraph.add_nodes_from"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.add_nodes_from</span></code></a>(nodes_for_adding, **attr)</p></td>
<td><p>Add multiple nodes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.remove_node.html#networkx.DiGraph.remove_node" title="networkx.DiGraph.remove_node"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.remove_node</span></code></a>(n)</p></td>
<td><p>Remove node n.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.remove_nodes_from.html#networkx.DiGraph.remove_nodes_from" title="networkx.DiGraph.remove_nodes_from"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.remove_nodes_from</span></code></a>(nodes)</p></td>
<td><p>Remove multiple nodes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.add_edge.html#networkx.DiGraph.add_edge" title="networkx.DiGraph.add_edge"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.add_edge</span></code></a>(u_of_edge, v_of_edge, **attr)</p></td>
<td><p>Add an edge between u and v.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.add_edges_from.html#networkx.DiGraph.add_edges_from" title="networkx.DiGraph.add_edges_from"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.add_edges_from</span></code></a>(ebunch_to_add, **attr)</p></td>
<td><p>Add all the edges in ebunch_to_add.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.add_weighted_edges_from.html#networkx.DiGraph.add_weighted_edges_from" title="networkx.DiGraph.add_weighted_edges_from"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.add_weighted_edges_from</span></code></a>(ebunch_to_add)</p></td>
<td><p>Add weighted edges in <code class="xref py py-obj docutils literal notranslate"><span class="pre">ebunch_to_add</span></code> with specified weight attr</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.remove_edge.html#networkx.DiGraph.remove_edge" title="networkx.DiGraph.remove_edge"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.remove_edge</span></code></a>(u, v)</p></td>
<td><p>Remove the edge between u and v.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.remove_edges_from.html#networkx.DiGraph.remove_edges_from" title="networkx.DiGraph.remove_edges_from"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.remove_edges_from</span></code></a>(ebunch)</p></td>
<td><p>Remove all edges specified in ebunch.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.update.html#networkx.DiGraph.update" title="networkx.DiGraph.update"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.update</span></code></a>([edges, nodes])</p></td>
<td><p>Update the graph using nodes/edges/graphs as input.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.clear.html#networkx.DiGraph.clear" title="networkx.DiGraph.clear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.clear</span></code></a>()</p></td>
<td><p>Remove all nodes and edges from the graph.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.clear_edges.html#networkx.DiGraph.clear_edges" title="networkx.DiGraph.clear_edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.clear_edges</span></code></a>()</p></td>
<td><p>Remove all edges from the graph without altering nodes.</p></td>
</tr>
</tbody>
</table>
</section>
<section id="reporting-nodes-edges-and-neighbors">
<h3>Reporting nodes edges and neighbors<a class="headerlink" href="#reporting-nodes-edges-and-neighbors" title="Permalink to this heading">#</a></h3>
<table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.nodes.html#networkx.DiGraph.nodes" title="networkx.DiGraph.nodes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.nodes</span></code></a></p></td>
<td><p>A NodeView of the Graph as G.nodes or G.nodes().</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.__iter__.html#networkx.DiGraph.__iter__" title="networkx.DiGraph.__iter__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.__iter__</span></code></a>()</p></td>
<td><p>Iterate over the nodes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.has_node.html#networkx.DiGraph.has_node" title="networkx.DiGraph.has_node"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.has_node</span></code></a>(n)</p></td>
<td><p>Returns True if the graph contains the node n.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.__contains__.html#networkx.DiGraph.__contains__" title="networkx.DiGraph.__contains__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.__contains__</span></code></a>(n)</p></td>
<td><p>Returns True if n is a node, False otherwise.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.edges.html#networkx.DiGraph.edges" title="networkx.DiGraph.edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.edges</span></code></a></p></td>
<td><p>An OutEdgeView of the DiGraph as G.edges or G.edges().</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.out_edges.html#networkx.DiGraph.out_edges" title="networkx.DiGraph.out_edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.out_edges</span></code></a></p></td>
<td><p>An OutEdgeView of the DiGraph as G.edges or G.edges().</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.in_edges.html#networkx.DiGraph.in_edges" title="networkx.DiGraph.in_edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.in_edges</span></code></a></p></td>
<td><p>A view of the in edges of the graph as G.in_edges or G.in_edges().</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.has_edge.html#networkx.DiGraph.has_edge" title="networkx.DiGraph.has_edge"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.has_edge</span></code></a>(u, v)</p></td>
<td><p>Returns True if the edge (u, v) is in the graph.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.get_edge_data.html#networkx.DiGraph.get_edge_data" title="networkx.DiGraph.get_edge_data"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.get_edge_data</span></code></a>(u, v[, default])</p></td>
<td><p>Returns the attribute dictionary associated with edge (u, v).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.neighbors.html#networkx.DiGraph.neighbors" title="networkx.DiGraph.neighbors"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.neighbors</span></code></a>(n)</p></td>
<td><p>Returns an iterator over successor nodes of n.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.adj.html#networkx.DiGraph.adj" title="networkx.DiGraph.adj"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.adj</span></code></a></p></td>
<td><p>Graph adjacency object holding the neighbors of each node.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.__getitem__.html#networkx.DiGraph.__getitem__" title="networkx.DiGraph.__getitem__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.__getitem__</span></code></a>(n)</p></td>
<td><p>Returns a dict of neighbors of node n.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.successors.html#networkx.DiGraph.successors" title="networkx.DiGraph.successors"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.successors</span></code></a>(n)</p></td>
<td><p>Returns an iterator over successor nodes of n.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.succ.html#networkx.DiGraph.succ" title="networkx.DiGraph.succ"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.succ</span></code></a></p></td>
<td><p>Graph adjacency object holding the successors of each node.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.predecessors.html#networkx.DiGraph.predecessors" title="networkx.DiGraph.predecessors"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.predecessors</span></code></a>(n)</p></td>
<td><p>Returns an iterator over predecessor nodes of n.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.pred.html#networkx.DiGraph.pred" title="networkx.DiGraph.pred"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.pred</span></code></a></p></td>
<td><p>Graph adjacency object holding the predecessors of each node.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.adjacency.html#networkx.DiGraph.adjacency" title="networkx.DiGraph.adjacency"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.adjacency</span></code></a>()</p></td>
<td><p>Returns an iterator over (node, adjacency dict) tuples for all nodes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.nbunch_iter.html#networkx.DiGraph.nbunch_iter" title="networkx.DiGraph.nbunch_iter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.nbunch_iter</span></code></a>([nbunch])</p></td>
<td><p>Returns an iterator over nodes contained in nbunch that are also in the graph.</p></td>
</tr>
</tbody>
</table>
</section>
<section id="counting-nodes-edges-and-neighbors">
<h3>Counting nodes edges and neighbors<a class="headerlink" href="#counting-nodes-edges-and-neighbors" title="Permalink to this heading">#</a></h3>
<table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.order.html#networkx.DiGraph.order" title="networkx.DiGraph.order"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.order</span></code></a>()</p></td>
<td><p>Returns the number of nodes in the graph.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.number_of_nodes.html#networkx.DiGraph.number_of_nodes" title="networkx.DiGraph.number_of_nodes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.number_of_nodes</span></code></a>()</p></td>
<td><p>Returns the number of nodes in the graph.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.__len__.html#networkx.DiGraph.__len__" title="networkx.DiGraph.__len__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.__len__</span></code></a>()</p></td>
<td><p>Returns the number of nodes in the graph.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.degree.html#networkx.DiGraph.degree" title="networkx.DiGraph.degree"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.degree</span></code></a></p></td>
<td><p>A DegreeView for the Graph as G.degree or G.degree().</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.in_degree.html#networkx.DiGraph.in_degree" title="networkx.DiGraph.in_degree"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.in_degree</span></code></a></p></td>
<td><p>An InDegreeView for (node, in_degree) or in_degree for single node.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.out_degree.html#networkx.DiGraph.out_degree" title="networkx.DiGraph.out_degree"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.out_degree</span></code></a></p></td>
<td><p>An OutDegreeView for (node, out_degree)</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.size.html#networkx.DiGraph.size" title="networkx.DiGraph.size"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.size</span></code></a>([weight])</p></td>
<td><p>Returns the number of edges or total of all edge weights.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.number_of_edges.html#networkx.DiGraph.number_of_edges" title="networkx.DiGraph.number_of_edges"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.number_of_edges</span></code></a>([u, v])</p></td>
<td><p>Returns the number of edges between two nodes.</p></td>
</tr>
</tbody>
</table>
</section>
<section id="making-copies-and-subgraphs">
<h3>Making copies and subgraphs<a class="headerlink" href="#making-copies-and-subgraphs" title="Permalink to this heading">#</a></h3>
<table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.copy.html#networkx.DiGraph.copy" title="networkx.DiGraph.copy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.copy</span></code></a>([as_view])</p></td>
<td><p>Returns a copy of the graph.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.to_undirected.html#networkx.DiGraph.to_undirected" title="networkx.DiGraph.to_undirected"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.to_undirected</span></code></a>([reciprocal, as_view])</p></td>
<td><p>Returns an undirected representation of the digraph.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.to_directed.html#networkx.DiGraph.to_directed" title="networkx.DiGraph.to_directed"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.to_directed</span></code></a>([as_view])</p></td>
<td><p>Returns a directed representation of the graph.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.subgraph.html#networkx.DiGraph.subgraph" title="networkx.DiGraph.subgraph"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.subgraph</span></code></a>(nodes)</p></td>
<td><p>Returns a SubGraph view of the subgraph induced on <code class="xref py py-obj docutils literal notranslate"><span class="pre">nodes</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/networkx.DiGraph.edge_subgraph.html#networkx.DiGraph.edge_subgraph" title="networkx.DiGraph.edge_subgraph"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.edge_subgraph</span></code></a>(edges)</p></td>
<td><p>Returns the subgraph induced by the specified edges.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/networkx.DiGraph.reverse.html#networkx.DiGraph.reverse" title="networkx.DiGraph.reverse"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiGraph.reverse</span></code></a>([copy])</p></td>
<td><p>Returns the reverse of the graph.</p></td>
</tr>
</tbody>
</table>
</section>
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Adding and removing nodes and edges
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Reporting nodes edges and neighbors
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Counting nodes edges and neighbors
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Making copies and subgraphs
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