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<h1>Source code for networkx.generators.directed</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Generators for some directed graphs, including growing network (GN) graphs and</span>
<span class="sd">scale-free graphs.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numbers</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="kn">from</span> <span class="nn">networkx.generators.classic</span> <span class="kn">import</span> <span class="n">empty_graph</span>
<span class="kn">from</span> <span class="nn">networkx.utils</span> <span class="kn">import</span> <span class="n">discrete_sequence</span><span class="p">,</span> <span class="n">py_random_state</span><span class="p">,</span> <span class="n">weighted_choice</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"gn_graph"</span><span class="p">,</span>
<span class="s2">"gnc_graph"</span><span class="p">,</span>
<span class="s2">"gnr_graph"</span><span class="p">,</span>
<span class="s2">"random_k_out_graph"</span><span class="p">,</span>
<span class="s2">"scale_free_graph"</span><span class="p">,</span>
<span class="p">]</span>
<div class="viewcode-block" id="gn_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.directed.gn_graph.html#networkx.generators.directed.gn_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">gn_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">create_using</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns the growing network (GN) digraph with `n` nodes.</span>
<span class="sd"> The GN graph is built by adding nodes one at a time with a link to one</span>
<span class="sd"> previously added node. The target node for the link is chosen with</span>
<span class="sd"> probability based on degree. The default attachment kernel is a linear</span>
<span class="sd"> function of the degree of a node.</span>
<span class="sd"> The graph is always a (directed) tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : int</span>
<span class="sd"> The number of nodes for the generated graph.</span>
<span class="sd"> kernel : function</span>
<span class="sd"> The attachment kernel.</span>
<span class="sd"> create_using : NetworkX graph constructor, optional (default DiGraph)</span>
<span class="sd"> Graph type to create. If graph instance, then cleared before populated.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> To create the undirected GN graph, use the :meth:`~DiGraph.to_directed`</span>
<span class="sd"> method::</span>
<span class="sd"> >>> D = nx.gn_graph(10) # the GN graph</span>
<span class="sd"> >>> G = D.to_undirected() # the undirected version</span>
<span class="sd"> To specify an attachment kernel, use the `kernel` keyword argument::</span>
<span class="sd"> >>> D = nx.gn_graph(10, kernel=lambda x: x ** 1.5) # A_k = k^1.5</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] P. L. Krapivsky and S. Redner,</span>
<span class="sd"> Organization of Growing Random Networks,</span>
<span class="sd"> Phys. Rev. E, 63, 066123, 2001.</span>
<span class="sd"> """</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">empty_graph</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">create_using</span><span class="p">,</span> <span class="n">default</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="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s2">"create_using must indicate a Directed Graph"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">kernel</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">kernel</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">G</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">0</span><span class="p">)</span> <span class="c1"># get started</span>
<span class="n">ds</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="c1"># degree sequence</span>
<span class="k">for</span> <span class="n">source</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="c1"># compute distribution from kernel and degree</span>
<span class="n">dist</span> <span class="o">=</span> <span class="p">[</span><span class="n">kernel</span><span class="p">(</span><span class="n">d</span><span class="p">)</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">ds</span><span class="p">]</span>
<span class="c1"># choose target from discrete distribution</span>
<span class="n">target</span> <span class="o">=</span> <span class="n">discrete_sequence</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">distribution</span><span class="o">=</span><span class="n">dist</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">ds</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># the source has only one link (degree one)</span>
<span class="n">ds</span><span class="p">[</span><span class="n">target</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span> <span class="c1"># add one to the target link degree</span>
<span class="k">return</span> <span class="n">G</span></div>
<div class="viewcode-block" id="gnr_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.directed.gnr_graph.html#networkx.generators.directed.gnr_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">gnr_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">create_using</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns the growing network with redirection (GNR) digraph with `n`</span>
<span class="sd"> nodes and redirection probability `p`.</span>
<span class="sd"> The GNR graph is built by adding nodes one at a time with a link to one</span>
<span class="sd"> previously added node. The previous target node is chosen uniformly at</span>
<span class="sd"> random. With probabiliy `p` the link is instead "redirected" to the</span>
<span class="sd"> successor node of the target.</span>
<span class="sd"> The graph is always a (directed) tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : int</span>
<span class="sd"> The number of nodes for the generated graph.</span>
<span class="sd"> p : float</span>
<span class="sd"> The redirection probability.</span>
<span class="sd"> create_using : NetworkX graph constructor, optional (default DiGraph)</span>
<span class="sd"> Graph type to create. If graph instance, then cleared before populated.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> To create the undirected GNR graph, use the :meth:`~DiGraph.to_directed`</span>
<span class="sd"> method::</span>
<span class="sd"> >>> D = nx.gnr_graph(10, 0.5) # the GNR graph</span>
<span class="sd"> >>> G = D.to_undirected() # the undirected version</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] P. L. Krapivsky and S. Redner,</span>
<span class="sd"> Organization of Growing Random Networks,</span>
<span class="sd"> Phys. Rev. E, 63, 066123, 2001.</span>
<span class="sd"> """</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">empty_graph</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">create_using</span><span class="p">,</span> <span class="n">default</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="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s2">"create_using must indicate a Directed Graph"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">G</span>
<span class="k">for</span> <span class="n">source</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="n">target</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">source</span><span class="p">)</span>
<span class="k">if</span> <span class="n">seed</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="o"><</span> <span class="n">p</span> <span class="ow">and</span> <span class="n">target</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="nb">next</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">successors</span><span class="p">(</span><span class="n">target</span><span class="p">))</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="k">return</span> <span class="n">G</span></div>
<div class="viewcode-block" id="gnc_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.directed.gnc_graph.html#networkx.generators.directed.gnc_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">gnc_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">create_using</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns the growing network with copying (GNC) digraph with `n` nodes.</span>
<span class="sd"> The GNC graph is built by adding nodes one at a time with a link to one</span>
<span class="sd"> previously added node (chosen uniformly at random) and to all of that</span>
<span class="sd"> node's successors.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : int</span>
<span class="sd"> The number of nodes for the generated graph.</span>
<span class="sd"> create_using : NetworkX graph constructor, optional (default DiGraph)</span>
<span class="sd"> Graph type to create. If graph instance, then cleared before populated.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] P. L. Krapivsky and S. Redner,</span>
<span class="sd"> Network Growth by Copying,</span>
<span class="sd"> Phys. Rev. E, 71, 036118, 2005k.},</span>
<span class="sd"> """</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">empty_graph</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">create_using</span><span class="p">,</span> <span class="n">default</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="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s2">"create_using must indicate a Directed Graph"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">G</span>
<span class="k">for</span> <span class="n">source</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="n">target</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">source</span><span class="p">)</span>
<span class="k">for</span> <span class="n">succ</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">successors</span><span class="p">(</span><span class="n">target</span><span class="p">):</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">succ</span><span class="p">)</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="k">return</span> <span class="n">G</span></div>
<div class="viewcode-block" id="scale_free_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.directed.scale_free_graph.html#networkx.generators.directed.scale_free_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">scale_free_graph</span><span class="p">(</span>
<span class="n">n</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.41</span><span class="p">,</span>
<span class="n">beta</span><span class="o">=</span><span class="mf">0.54</span><span class="p">,</span>
<span class="n">gamma</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span>
<span class="n">delta_in</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">delta_out</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="n">create_using</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">initial_graph</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a scale-free directed graph.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : integer</span>
<span class="sd"> Number of nodes in graph</span>
<span class="sd"> alpha : float</span>
<span class="sd"> Probability for adding a new node connected to an existing node</span>
<span class="sd"> chosen randomly according to the in-degree distribution.</span>
<span class="sd"> beta : float</span>
<span class="sd"> Probability for adding an edge between two existing nodes.</span>
<span class="sd"> One existing node is chosen randomly according the in-degree</span>
<span class="sd"> distribution and the other chosen randomly according to the out-degree</span>
<span class="sd"> distribution.</span>
<span class="sd"> gamma : float</span>
<span class="sd"> Probability for adding a new node connected to an existing node</span>
<span class="sd"> chosen randomly according to the out-degree distribution.</span>
<span class="sd"> delta_in : float</span>
<span class="sd"> Bias for choosing nodes from in-degree distribution.</span>
<span class="sd"> delta_out : float</span>
<span class="sd"> Bias for choosing nodes from out-degree distribution.</span>
<span class="sd"> create_using : NetworkX graph constructor, optional</span>
<span class="sd"> The default is a MultiDiGraph 3-cycle.</span>
<span class="sd"> If a graph instance, use it without clearing first.</span>
<span class="sd"> If a graph constructor, call it to construct an empty graph.</span>
<span class="sd"> .. deprecated:: 3.0</span>
<span class="sd"> create_using is deprecated, use `initial_graph` instead.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> initial_graph : MultiDiGraph instance, optional</span>
<span class="sd"> Build the scale-free graph starting from this initial MultiDiGraph,</span>
<span class="sd"> if provided.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> MultiDiGraph</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> Create a scale-free graph on one hundred nodes::</span>
<span class="sd"> >>> G = nx.scale_free_graph(100)</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The sum of `alpha`, `beta`, and `gamma` must be 1.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan,</span>
<span class="sd"> Directed scale-free graphs,</span>
<span class="sd"> Proceedings of the fourteenth annual ACM-SIAM Symposium on</span>
<span class="sd"> Discrete Algorithms, 132--139, 2003.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">_choose_node</span><span class="p">(</span><span class="n">candidates</span><span class="p">,</span> <span class="n">node_list</span><span class="p">,</span> <span class="n">delta</span><span class="p">):</span>
<span class="k">if</span> <span class="n">delta</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">bias_sum</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">node_list</span><span class="p">)</span> <span class="o">*</span> <span class="n">delta</span>
<span class="n">p_delta</span> <span class="o">=</span> <span class="n">bias_sum</span> <span class="o">/</span> <span class="p">(</span><span class="n">bias_sum</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">candidates</span><span class="p">))</span>
<span class="k">if</span> <span class="n">seed</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="o"><</span> <span class="n">p_delta</span><span class="p">:</span>
<span class="k">return</span> <span class="n">seed</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">node_list</span><span class="p">)</span>
<span class="k">return</span> <span class="n">seed</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">candidates</span><span class="p">)</span>
<span class="k">if</span> <span class="n">create_using</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
<span class="s2">"The create_using argument is deprecated and will be removed in the future.</span><span class="se">\n\n</span><span class="s2">"</span>
<span class="s2">"To create a scale free graph from an existing MultiDiGraph, use</span><span class="se">\n</span><span class="s2">"</span>
<span class="s2">"initial_graph instead."</span><span class="p">,</span>
<span class="ne">DeprecationWarning</span><span class="p">,</span>
<span class="n">stacklevel</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="p">)</span>
<span class="c1"># TODO: Rm all this complicated logic when deprecation expires and replace</span>
<span class="c1"># with commented code:</span>
<span class="c1"># if initial_graph is not None and hasattr(initial_graph, "_adj"):</span>
<span class="c1"># G = initial_graph</span>
<span class="c1"># else:</span>
<span class="c1"># # Start with 3-cycle</span>
<span class="c1"># G = nx.MultiDiGraph([(0, 1), (1, 2), (2, 0)])</span>
<span class="k">if</span> <span class="n">create_using</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">create_using</span><span class="p">,</span> <span class="s2">"_adj"</span><span class="p">):</span>
<span class="k">if</span> <span class="n">initial_graph</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
<span class="s2">"Cannot set both create_using and initial_graph. Set create_using=None."</span>
<span class="p">)</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">create_using</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">initial_graph</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">initial_graph</span><span class="p">,</span> <span class="s2">"_adj"</span><span class="p">):</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">initial_graph</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">MultiDiGraph</span><span class="p">([(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</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">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)])</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">()</span> <span class="ow">and</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</span><span class="p">()):</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s2">"MultiDiGraph required in initial_graph"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">alpha</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"alpha must be > 0."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">beta</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"beta must be > 0."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">gamma</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"gamma must be > 0."</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">alpha</span> <span class="o">+</span> <span class="n">beta</span> <span class="o">+</span> <span class="n">gamma</span> <span class="o">-</span> <span class="mf">1.0</span><span class="p">)</span> <span class="o">>=</span> <span class="mf">1e-9</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"alpha+beta+gamma must equal 1."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">delta_in</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"delta_in must be >= 0."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">delta_out</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"delta_out must be >= 0."</span><span class="p">)</span>
<span class="c1"># pre-populate degree states</span>
<span class="n">vs</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">((</span><span class="n">count</span> <span class="o">*</span> <span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">count</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">out_degree</span><span class="p">()),</span> <span class="p">[])</span>
<span class="n">ws</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">((</span><span class="n">count</span> <span class="o">*</span> <span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">count</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">in_degree</span><span class="p">()),</span> <span class="p">[])</span>
<span class="c1"># pre-populate node state</span>
<span class="n">node_list</span> <span class="o">=</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="c1"># see if there already are number-based nodes</span>
<span class="n">numeric_nodes</span> <span class="o">=</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">node_list</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">)]</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">numeric_nodes</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># set cursor for new nodes appropriately</span>
<span class="n">cursor</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">real</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">numeric_nodes</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># or start at zero</span>
<span class="n">cursor</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="o"><</span> <span class="n">n</span><span class="p">:</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
<span class="c1"># random choice in alpha,beta,gamma ranges</span>
<span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="n">alpha</span><span class="p">:</span>
<span class="c1"># alpha</span>
<span class="c1"># add new node v</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">cursor</span>
<span class="n">cursor</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># also add to node state</span>
<span class="n">node_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="c1"># choose w according to in-degree and delta_in</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">_choose_node</span><span class="p">(</span><span class="n">ws</span><span class="p">,</span> <span class="n">node_list</span><span class="p">,</span> <span class="n">delta_in</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">r</span> <span class="o"><</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">beta</span><span class="p">:</span>
<span class="c1"># beta</span>
<span class="c1"># choose v according to out-degree and delta_out</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_choose_node</span><span class="p">(</span><span class="n">vs</span><span class="p">,</span> <span class="n">node_list</span><span class="p">,</span> <span class="n">delta_out</span><span class="p">)</span>
<span class="c1"># choose w according to in-degree and delta_in</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">_choose_node</span><span class="p">(</span><span class="n">ws</span><span class="p">,</span> <span class="n">node_list</span><span class="p">,</span> <span class="n">delta_in</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># gamma</span>
<span class="c1"># choose v according to out-degree and delta_out</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_choose_node</span><span class="p">(</span><span class="n">vs</span><span class="p">,</span> <span class="n">node_list</span><span class="p">,</span> <span class="n">delta_out</span><span class="p">)</span>
<span class="c1"># add new node w</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">cursor</span>
<span class="n">cursor</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># also add to node state</span>
<span class="n">node_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="c1"># add edge to graph</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">w</span><span class="p">)</span>
<span class="c1"># update degree states</span>
<span class="n">vs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">ws</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="k">return</span> <span class="n">G</span></div>
<span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">random_uniform_k_out_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">self_loops</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">with_replacement</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a random `k`-out graph with uniform attachment.</span>
<span class="sd"> A random `k`-out graph with uniform attachment is a multidigraph</span>
<span class="sd"> generated by the following algorithm. For each node *u*, choose</span>
<span class="sd"> `k` nodes *v* uniformly at random (with replacement). Add a</span>
<span class="sd"> directed edge joining *u* to *v*.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : int</span>
<span class="sd"> The number of nodes in the returned graph.</span>
<span class="sd"> k : int</span>
<span class="sd"> The out-degree of each node in the returned graph.</span>
<span class="sd"> self_loops : bool</span>
<span class="sd"> If True, self-loops are allowed when generating the graph.</span>
<span class="sd"> with_replacement : bool</span>
<span class="sd"> If True, neighbors are chosen with replacement and the</span>
<span class="sd"> returned graph will be a directed multigraph. Otherwise,</span>
<span class="sd"> neighbors are chosen without replacement and the returned graph</span>
<span class="sd"> will be a directed graph.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> NetworkX graph</span>
<span class="sd"> A `k`-out-regular directed graph generated according to the</span>
<span class="sd"> above algorithm. It will be a multigraph if and only if</span>
<span class="sd"> `with_replacement` is True.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> ValueError</span>
<span class="sd"> If `with_replacement` is False and `k` is greater than</span>
<span class="sd"> `n`.</span>
<span class="sd"> See also</span>
<span class="sd"> --------</span>
<span class="sd"> random_k_out_graph</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The return digraph or multidigraph may not be strongly connected, or</span>
<span class="sd"> even weakly connected.</span>
<span class="sd"> If `with_replacement` is True, this function is similar to</span>
<span class="sd"> :func:`random_k_out_graph`, if that function had parameter `alpha`</span>
<span class="sd"> set to positive infinity.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">with_replacement</span><span class="p">:</span>
<span class="n">create_using</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">MultiDiGraph</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">nodes</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">self_loops</span><span class="p">:</span>
<span class="n">nodes</span> <span class="o">=</span> <span class="n">nodes</span> <span class="o">-</span> <span class="p">{</span><span class="n">v</span><span class="p">}</span>
<span class="k">return</span> <span class="p">(</span><span class="n">seed</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">nodes</span><span class="p">))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">create_using</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="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">nodes</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">self_loops</span><span class="p">:</span>
<span class="n">nodes</span> <span class="o">=</span> <span class="n">nodes</span> <span class="o">-</span> <span class="p">{</span><span class="n">v</span><span class="p">}</span>
<span class="k">return</span> <span class="n">seed</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">nodes</span><span class="p">),</span> <span class="n">k</span><span class="p">)</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">empty_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">create_using</span><span class="p">)</span>
<span class="n">nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">((</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">sample</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">nodes</span><span class="p">))</span>
<span class="k">return</span> <span class="n">G</span>
<div class="viewcode-block" id="random_k_out_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.directed.random_k_out_graph.html#networkx.generators.directed.random_k_out_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">random_k_out_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">self_loops</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a random `k`-out graph with preferential attachment.</span>
<span class="sd"> A random `k`-out graph with preferential attachment is a</span>
<span class="sd"> multidigraph generated by the following algorithm.</span>
<span class="sd"> 1. Begin with an empty digraph, and initially set each node to have</span>
<span class="sd"> weight `alpha`.</span>
<span class="sd"> 2. Choose a node `u` with out-degree less than `k` uniformly at</span>
<span class="sd"> random.</span>
<span class="sd"> 3. Choose a node `v` from with probability proportional to its</span>
<span class="sd"> weight.</span>
<span class="sd"> 4. Add a directed edge from `u` to `v`, and increase the weight</span>
<span class="sd"> of `v` by one.</span>
<span class="sd"> 5. If each node has out-degree `k`, halt, otherwise repeat from</span>
<span class="sd"> step 2.</span>
<span class="sd"> For more information on this model of random graph, see [1].</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n : int</span>
<span class="sd"> The number of nodes in the returned graph.</span>
<span class="sd"> k : int</span>
<span class="sd"> The out-degree of each node in the returned graph.</span>
<span class="sd"> alpha : float</span>
<span class="sd"> A positive :class:`float` representing the initial weight of</span>
<span class="sd"> each vertex. A higher number means that in step 3 above, nodes</span>
<span class="sd"> will be chosen more like a true uniformly random sample, and a</span>
<span class="sd"> lower number means that nodes are more likely to be chosen as</span>
<span class="sd"> their in-degree increases. If this parameter is not positive, a</span>
<span class="sd"> :exc:`ValueError` is raised.</span>
<span class="sd"> self_loops : bool</span>
<span class="sd"> If True, self-loops are allowed when generating the graph.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> :class:`~networkx.classes.MultiDiGraph`</span>
<span class="sd"> A `k`-out-regular multidigraph generated according to the above</span>
<span class="sd"> algorithm.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> ValueError</span>
<span class="sd"> If `alpha` is not positive.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The returned multidigraph may not be strongly connected, or even</span>
<span class="sd"> weakly connected.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1]: Peterson, Nicholas R., and Boris Pittel.</span>
<span class="sd"> "Distance between two random `k`-out digraphs, with and without</span>
<span class="sd"> preferential attachment."</span>
<span class="sd"> arXiv preprint arXiv:1311.5961 (2013).</span>
<span class="sd"> <https://arxiv.org/abs/1311.5961></span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">alpha</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"alpha must be positive"</span><span class="p">)</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">empty_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">create_using</span><span class="o">=</span><span class="n">nx</span><span class="o">.</span><span class="n">MultiDiGraph</span><span class="p">)</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">({</span><span class="n">v</span><span class="p">:</span> <span class="n">alpha</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">G</span><span class="p">})</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">choice</span><span class="p">([</span><span class="n">v</span> <span class="k">for</span> <span class="n">v</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">out_degree</span><span class="p">()</span> <span class="k">if</span> <span class="n">d</span> <span class="o"><</span> <span class="n">k</span><span class="p">])</span>
<span class="c1"># If self-loops are not allowed, make the source node `u` have</span>
<span class="c1"># weight zero.</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">self_loops</span><span class="p">:</span>
<span class="n">adjustment</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">({</span><span class="n">u</span><span class="p">:</span> <span class="n">weights</span><span class="p">[</span><span class="n">u</span><span class="p">]})</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">adjustment</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">weighted_choice</span><span class="p">(</span><span class="n">weights</span> <span class="o">-</span> <span class="n">adjustment</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
<span class="n">weights</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">G</span></div>
</pre></div>
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