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<h1>Source code for networkx.generators.joint_degree_seq</h1><div class="highlight"><pre>
<span></span><span class="sd">"""Generate graphs with a given joint degree and directed joint degree"""</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.utils</span> <span class="kn">import</span> <span class="n">py_random_state</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"is_valid_joint_degree"</span><span class="p">,</span>
<span class="s2">"is_valid_directed_joint_degree"</span><span class="p">,</span>
<span class="s2">"joint_degree_graph"</span><span class="p">,</span>
<span class="s2">"directed_joint_degree_graph"</span><span class="p">,</span>
<span class="p">]</span>
<div class="viewcode-block" id="is_valid_joint_degree"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.joint_degree_seq.is_valid_joint_degree.html#networkx.generators.joint_degree_seq.is_valid_joint_degree">[docs]</a><span class="k">def</span> <span class="nf">is_valid_joint_degree</span><span class="p">(</span><span class="n">joint_degrees</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Checks whether the given joint degree dictionary is realizable.</span>
<span class="sd"> A *joint degree dictionary* is a dictionary of dictionaries, in</span>
<span class="sd"> which entry ``joint_degrees[k][l]`` is an integer representing the</span>
<span class="sd"> number of edges joining nodes of degree *k* with nodes of degree</span>
<span class="sd"> *l*. Such a dictionary is realizable as a simple graph if and only</span>
<span class="sd"> if the following conditions are satisfied.</span>
<span class="sd"> - each entry must be an integer,</span>
<span class="sd"> - the total number of nodes of degree *k*, computed by</span>
<span class="sd"> ``sum(joint_degrees[k].values()) / k``, must be an integer,</span>
<span class="sd"> - the total number of edges joining nodes of degree *k* with</span>
<span class="sd"> nodes of degree *l* cannot exceed the total number of possible edges,</span>
<span class="sd"> - each diagonal entry ``joint_degrees[k][k]`` must be even (this is</span>
<span class="sd"> a convention assumed by the :func:`joint_degree_graph` function).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> joint_degrees : dictionary of dictionary of integers</span>
<span class="sd"> A joint degree dictionary in which entry ``joint_degrees[k][l]``</span>
<span class="sd"> is the number of edges joining nodes of degree *k* with nodes of</span>
<span class="sd"> degree *l*.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> bool</span>
<span class="sd"> Whether the given joint degree dictionary is realizable as a</span>
<span class="sd"> simple graph.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] M. Gjoka, M. Kurant, A. Markopoulou, "2.5K Graphs: from Sampling</span>
<span class="sd"> to Generation", IEEE Infocom, 2013.</span>
<span class="sd"> .. [2] I. Stanton, A. Pinar, "Constructing and sampling graphs with a</span>
<span class="sd"> prescribed joint degree distribution", Journal of Experimental</span>
<span class="sd"> Algorithmics, 2012.</span>
<span class="sd"> """</span>
<span class="n">degree_count</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="p">:</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">k_size</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="o">.</span><span class="n">values</span><span class="p">())</span> <span class="o">/</span> <span class="n">k</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">k_size</span><span class="o">.</span><span class="n">is_integer</span><span class="p">():</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="n">degree_count</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">k_size</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="p">:</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">float</span><span class="p">(</span><span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">])</span><span class="o">.</span><span class="n">is_integer</span><span class="p">():</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="p">(</span><span class="n">k</span> <span class="o">!=</span> <span class="n">l</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="n">degree_count</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">degree_count</span><span class="p">[</span><span class="n">l</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="n">k</span> <span class="o">==</span> <span class="n">l</span><span class="p">:</span>
<span class="k">if</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">k</span><span class="p">]</span> <span class="o">></span> <span class="n">degree_count</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">degree_count</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">k</span><span class="p">]</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># if all above conditions have been satisfied then the input</span>
<span class="c1"># joint degree is realizable as a simple graph.</span>
<span class="k">return</span> <span class="kc">True</span></div>
<span class="k">def</span> <span class="nf">_neighbor_switch</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">unsat</span><span class="p">,</span> <span class="n">h_node_residual</span><span class="p">,</span> <span class="n">avoid_node_id</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Releases one free stub for ``w``, while preserving joint degree in G.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> Graph in which the neighbor switch will take place.</span>
<span class="sd"> w : integer</span>
<span class="sd"> Node id for which we will execute this neighbor switch.</span>
<span class="sd"> unsat : set of integers</span>
<span class="sd"> Set of unsaturated node ids that have the same degree as w.</span>
<span class="sd"> h_node_residual: dictionary of integers</span>
<span class="sd"> Keeps track of the remaining stubs for a given node.</span>
<span class="sd"> avoid_node_id: integer</span>
<span class="sd"> Node id to avoid when selecting w_prime.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> First, it selects *w_prime*, an unsaturated node that has the same degree</span>
<span class="sd"> as ``w``. Second, it selects *switch_node*, a neighbor node of ``w`` that</span>
<span class="sd"> is not connected to *w_prime*. Then it executes an edge swap i.e. removes</span>
<span class="sd"> (``w``,*switch_node*) and adds (*w_prime*,*switch_node*). Gjoka et. al. [1]</span>
<span class="sd"> prove that such an edge swap is always possible.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] M. Gjoka, B. Tillman, A. Markopoulou, "Construction of Simple</span>
<span class="sd"> Graphs with a Target Joint Degree Matrix and Beyond", IEEE Infocom, '15</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="p">(</span><span class="n">avoid_node_id</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">h_node_residual</span><span class="p">[</span><span class="n">avoid_node_id</span><span class="p">]</span> <span class="o">></span> <span class="mi">1</span><span class="p">):</span>
<span class="c1"># select unsatured node w_prime that has the same degree as w</span>
<span class="n">w_prime</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">unsat</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># assume that the node pair (v,w) has been selected for connection. if</span>
<span class="c1"># - neighbor_switch is called for node w,</span>
<span class="c1"># - nodes v and w have the same degree,</span>
<span class="c1"># - node v=avoid_node_id has only one stub left,</span>
<span class="c1"># then prevent v=avoid_node_id from being selected as w_prime.</span>
<span class="n">iter_var</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">unsat</span><span class="p">)</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">w_prime</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">iter_var</span><span class="p">)</span>
<span class="k">if</span> <span class="n">w_prime</span> <span class="o">!=</span> <span class="n">avoid_node_id</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># select switch_node, a neighbor of w, that is not connected to w_prime</span>
<span class="n">w_prime_neighbs</span> <span class="o">=</span> <span class="n">G</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="c1"># slightly faster declaring this variable</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="n">w</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">w_prime_neighbs</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">v</span> <span class="o">!=</span> <span class="n">w_prime</span><span class="p">):</span>
<span class="n">switch_node</span> <span class="o">=</span> <span class="n">v</span>
<span class="k">break</span>
<span class="c1"># remove edge (w,switch_node), add edge (w_prime,switch_node) and update</span>
<span class="c1"># data structures</span>
<span class="n">G</span><span class="o">.</span><span class="n">remove_edge</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">switch_node</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">w_prime</span><span class="p">,</span> <span class="n">switch_node</span><span class="p">)</span>
<span class="n">h_node_residual</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">h_node_residual</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">unsat</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">w_prime</span><span class="p">)</span>
<div class="viewcode-block" id="joint_degree_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.joint_degree_seq.joint_degree_graph.html#networkx.generators.joint_degree_seq.joint_degree_graph">[docs]</a><span class="nd">@py_random_state</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">joint_degree_graph</span><span class="p">(</span><span class="n">joint_degrees</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">"""Generates a random simple graph with the given joint degree dictionary.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> joint_degrees : dictionary of dictionary of integers</span>
<span class="sd"> A joint degree dictionary in which entry ``joint_degrees[k][l]`` is the</span>
<span class="sd"> number of edges joining nodes of degree *k* with nodes of degree *l*.</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"> G : Graph</span>
<span class="sd"> A graph with the specified joint degree dictionary.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> If *joint_degrees* dictionary is not realizable.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> In each iteration of the "while loop" the algorithm picks two disconnected</span>
<span class="sd"> nodes *v* and *w*, of degree *k* and *l* correspondingly, for which</span>
<span class="sd"> ``joint_degrees[k][l]`` has not reached its target yet. It then adds</span>
<span class="sd"> edge (*v*, *w*) and increases the number of edges in graph G by one.</span>
<span class="sd"> The intelligence of the algorithm lies in the fact that it is always</span>
<span class="sd"> possible to add an edge between such disconnected nodes *v* and *w*,</span>
<span class="sd"> even if one or both nodes do not have free stubs. That is made possible by</span>
<span class="sd"> executing a "neighbor switch", an edge rewiring move that releases</span>
<span class="sd"> a free stub while keeping the joint degree of G the same.</span>
<span class="sd"> The algorithm continues for E (number of edges) iterations of</span>
<span class="sd"> the "while loop", at the which point all entries of the given</span>
<span class="sd"> ``joint_degrees[k][l]`` have reached their target values and the</span>
<span class="sd"> construction is complete.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] M. Gjoka, B. Tillman, A. Markopoulou, "Construction of Simple</span>
<span class="sd"> Graphs with a Target Joint Degree Matrix and Beyond", IEEE Infocom, '15</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> joint_degrees = {</span>
<span class="sd"> ... 1: {4: 1},</span>
<span class="sd"> ... 2: {2: 2, 3: 2, 4: 2},</span>
<span class="sd"> ... 3: {2: 2, 4: 1},</span>
<span class="sd"> ... 4: {1: 1, 2: 2, 3: 1},</span>
<span class="sd"> ... }</span>
<span class="sd"> >>> G = nx.joint_degree_graph(joint_degrees)</span>
<span class="sd"> >>></span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_valid_joint_degree</span><span class="p">(</span><span class="n">joint_degrees</span><span class="p">):</span>
<span class="n">msg</span> <span class="o">=</span> <span class="s2">"Input joint degree dict not realizable as a simple graph"</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="n">msg</span><span class="p">)</span>
<span class="c1"># compute degree count from joint_degrees</span>
<span class="n">degree_count</span> <span class="o">=</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="nb">sum</span><span class="p">(</span><span class="n">l</span><span class="o">.</span><span class="n">values</span><span class="p">())</span> <span class="o">//</span> <span class="n">k</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="o">.</span><span class="n">items</span><span class="p">()</span> <span class="k">if</span> <span class="n">k</span> <span class="o">></span> <span class="mi">0</span><span class="p">}</span>
<span class="c1"># start with empty N-node graph</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">degree_count</span><span class="o">.</span><span class="n">values</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="c1"># for a given degree group, keep the list of all node ids</span>
<span class="n">h_degree_nodelist</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># for a given node, keep track of the remaining stubs</span>
<span class="n">h_node_residual</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># populate h_degree_nodelist and h_node_residual</span>
<span class="n">nodeid</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">degree</span><span class="p">,</span> <span class="n">num_nodes</span> <span class="ow">in</span> <span class="n">degree_count</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">h_degree_nodelist</span><span class="p">[</span><span class="n">degree</span><span class="p">]</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">nodeid</span><span class="p">,</span> <span class="n">nodeid</span> <span class="o">+</span> <span class="n">num_nodes</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">h_degree_nodelist</span><span class="p">[</span><span class="n">degree</span><span class="p">]:</span>
<span class="n">h_node_residual</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">degree</span>
<span class="n">nodeid</span> <span class="o">+=</span> <span class="nb">int</span><span class="p">(</span><span class="n">num_nodes</span><span class="p">)</span>
<span class="c1"># iterate over every degree pair (k,l) and add the number of edges given</span>
<span class="c1"># for each pair</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="p">:</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
<span class="c1"># n_edges_add is the number of edges to add for the</span>
<span class="c1"># degree pair (k,l)</span>
<span class="n">n_edges_add</span> <span class="o">=</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">]</span>
<span class="k">if</span> <span class="p">(</span><span class="n">n_edges_add</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">k</span> <span class="o">>=</span> <span class="n">l</span><span class="p">):</span>
<span class="c1"># number of nodes with degree k and l</span>
<span class="n">k_size</span> <span class="o">=</span> <span class="n">degree_count</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
<span class="n">l_size</span> <span class="o">=</span> <span class="n">degree_count</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
<span class="c1"># k_nodes and l_nodes consist of all nodes of degree k and l</span>
<span class="n">k_nodes</span> <span class="o">=</span> <span class="n">h_degree_nodelist</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
<span class="n">l_nodes</span> <span class="o">=</span> <span class="n">h_degree_nodelist</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
<span class="c1"># k_unsat and l_unsat consist of nodes of degree k and l that</span>
<span class="c1"># are unsaturated (nodes that have at least 1 available stub)</span>
<span class="n">k_unsat</span> <span class="o">=</span> <span class="p">{</span><span class="n">v</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">k_nodes</span> <span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">></span> <span class="mi">0</span><span class="p">}</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">!=</span> <span class="n">l</span><span class="p">:</span>
<span class="n">l_unsat</span> <span class="o">=</span> <span class="p">{</span><span class="n">w</span> <span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">l_nodes</span> <span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">></span> <span class="mi">0</span><span class="p">}</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">l_unsat</span> <span class="o">=</span> <span class="n">k_unsat</span>
<span class="n">n_edges_add</span> <span class="o">=</span> <span class="n">joint_degrees</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">]</span> <span class="o">//</span> <span class="mi">2</span>
<span class="k">while</span> <span class="n">n_edges_add</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># randomly pick nodes v and w that have degrees k and l</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">k_nodes</span><span class="p">[</span><span class="n">seed</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="n">k_size</span><span class="p">)]</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">l_nodes</span><span class="p">[</span><span class="n">seed</span><span class="o">.</span><span class="n">randrange</span><span class="p">(</span><span class="n">l_size</span><span class="p">)]</span>
<span class="c1"># if nodes v and w are disconnected then attempt to connect</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">has_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="ow">and</span> <span class="p">(</span><span class="n">v</span> <span class="o">!=</span> <span class="n">w</span><span class="p">):</span>
<span class="c1"># if node v has no free stubs then do neighbor switch</span>
<span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">_neighbor_switch</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">k_unsat</span><span class="p">,</span> <span class="n">h_node_residual</span><span class="p">)</span>
<span class="c1"># if node w has no free stubs then do neighbor switch</span>
<span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">!=</span> <span class="n">l</span><span class="p">:</span>
<span class="n">_neighbor_switch</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">l_unsat</span><span class="p">,</span> <span class="n">h_node_residual</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">_neighbor_switch</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">l_unsat</span><span class="p">,</span> <span class="n">h_node_residual</span><span class="p">,</span> <span class="n">avoid_node_id</span><span class="o">=</span><span class="n">v</span>
<span class="p">)</span>
<span class="c1"># add edge (v, w) and update data structures</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="n">h_node_residual</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="n">h_node_residual</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">n_edges_add</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">k_unsat</span><span class="o">.</span><span class="n">discard</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="n">h_node_residual</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">l_unsat</span><span class="o">.</span><span class="n">discard</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>
<div class="viewcode-block" id="is_valid_directed_joint_degree"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.joint_degree_seq.is_valid_directed_joint_degree.html#networkx.generators.joint_degree_seq.is_valid_directed_joint_degree">[docs]</a><span class="k">def</span> <span class="nf">is_valid_directed_joint_degree</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">,</span> <span class="n">out_degrees</span><span class="p">,</span> <span class="n">nkk</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Checks whether the given directed joint degree input is realizable</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> in_degrees : list of integers</span>
<span class="sd"> in degree sequence contains the in degrees of nodes.</span>
<span class="sd"> out_degrees : list of integers</span>
<span class="sd"> out degree sequence contains the out degrees of nodes.</span>
<span class="sd"> nkk : dictionary of dictionary of integers</span>
<span class="sd"> directed joint degree dictionary. for nodes of out degree k (first</span>
<span class="sd"> level of dict) and nodes of in degree l (seconnd level of dict)</span>
<span class="sd"> describes the number of edges.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> boolean</span>
<span class="sd"> returns true if given input is realizable, else returns false.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> Here is the list of conditions that the inputs (in/out degree sequences,</span>
<span class="sd"> nkk) need to satisfy for simple directed graph realizability:</span>
<span class="sd"> - Condition 0: in_degrees and out_degrees have the same length</span>
<span class="sd"> - Condition 1: nkk[k][l] is integer for all k,l</span>
<span class="sd"> - Condition 2: sum(nkk[k])/k = number of nodes with partition id k, is an</span>
<span class="sd"> integer and matching degree sequence</span>
<span class="sd"> - Condition 3: number of edges and non-chords between k and l cannot exceed</span>
<span class="sd"> maximum possible number of edges</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] B. Tillman, A. Markopoulou, C. T. Butts & M. Gjoka,</span>
<span class="sd"> "Construction of Directed 2K Graphs". In Proc. of KDD 2017.</span>
<span class="sd"> """</span>
<span class="n">V</span> <span class="o">=</span> <span class="p">{}</span> <span class="c1"># number of nodes with in/out degree.</span>
<span class="n">forbidden</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">out_degrees</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">)):</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">in_degrees</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">o</span> <span class="o">=</span> <span class="n">out_degrees</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">V</span><span class="p">[(</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="o">=</span> <span class="n">V</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">V</span><span class="p">[(</span><span class="n">o</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="o">=</span> <span class="n">V</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">o</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="o">+</span> <span class="mi">1</span>
<span class="n">forbidden</span><span class="p">[(</span><span class="n">o</span><span class="p">,</span> <span class="n">i</span><span class="p">)]</span> <span class="o">=</span> <span class="n">forbidden</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">o</span><span class="p">,</span> <span class="n">i</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">S</span> <span class="o">=</span> <span class="p">{}</span> <span class="c1"># number of edges going from in/out degree nodes.</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">nkk</span><span class="p">:</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">nkk</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
<span class="n">val</span> <span class="o">=</span> <span class="n">nkk</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">]</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">float</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="o">.</span><span class="n">is_integer</span><span class="p">():</span> <span class="c1"># condition 1</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="n">val</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">S</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="o">=</span> <span class="n">S</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">k</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="o">+</span> <span class="n">val</span>
<span class="n">S</span><span class="p">[(</span><span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="o">=</span> <span class="n">S</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">val</span>
<span class="c1"># condition 3</span>
<span class="k">if</span> <span class="n">val</span> <span class="o">+</span> <span class="n">forbidden</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">l</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">></span> <span class="n">V</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="o">*</span> <span class="n">V</span><span class="p">[(</span><span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]:</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">S</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">S</span><span class="p">[</span><span class="n">s</span><span class="p">]</span> <span class="o">/</span> <span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">V</span><span class="p">[</span><span class="n">s</span><span class="p">]:</span> <span class="c1"># condition 2</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># if all conditions abive have been satisfied then the input nkk is</span>
<span class="c1"># realizable as a simple graph.</span>
<span class="k">return</span> <span class="kc">True</span></div>
<span class="k">def</span> <span class="nf">_directed_neighbor_switch</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">unsat</span><span class="p">,</span> <span class="n">h_node_residual_out</span><span class="p">,</span> <span class="n">chords</span><span class="p">,</span> <span class="n">h_partition_in</span><span class="p">,</span> <span class="n">partition</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Releases one free stub for node w, while preserving joint degree in G.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : networkx directed graph</span>
<span class="sd"> graph within which the edge swap will take place.</span>
<span class="sd"> w : integer</span>
<span class="sd"> node id for which we need to perform a neighbor switch.</span>
<span class="sd"> unsat: set of integers</span>
<span class="sd"> set of node ids that have the same degree as w and are unsaturated.</span>
<span class="sd"> h_node_residual_out: dict of integers</span>
<span class="sd"> for a given node, keeps track of the remaining stubs to be added.</span>
<span class="sd"> chords: set of tuples</span>
<span class="sd"> keeps track of available positions to add edges.</span>
<span class="sd"> h_partition_in: dict of integers</span>
<span class="sd"> for a given node, keeps track of its partition id (in degree).</span>
<span class="sd"> partition: integer</span>
<span class="sd"> partition id to check if chords have to be updated.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> First, it selects node w_prime that (1) has the same degree as w and</span>
<span class="sd"> (2) is unsaturated. Then, it selects node v, a neighbor of w, that is</span>
<span class="sd"> not connected to w_prime and does an edge swap i.e. removes (w,v) and</span>
<span class="sd"> adds (w_prime,v). If neighbor switch is not possible for w using</span>
<span class="sd"> w_prime and v, then return w_prime; in [1] it's proven that</span>
<span class="sd"> such unsaturated nodes can be used.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] B. Tillman, A. Markopoulou, C. T. Butts & M. Gjoka,</span>
<span class="sd"> "Construction of Directed 2K Graphs". In Proc. of KDD 2017.</span>
<span class="sd"> """</span>
<span class="n">w_prime</span> <span class="o">=</span> <span class="n">unsat</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">unsat</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">w_prime</span><span class="p">)</span>
<span class="c1"># select node t, a neighbor of w, that is not connected to w_prime</span>
<span class="n">w_neighbs</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">successors</span><span class="p">(</span><span class="n">w</span><span class="p">))</span>
<span class="c1"># slightly faster declaring this variable</span>
<span class="n">w_prime_neighbs</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">successors</span><span class="p">(</span><span class="n">w_prime</span><span class="p">))</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">w_neighbs</span><span class="p">:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">w_prime_neighbs</span><span class="p">)</span> <span class="ow">and</span> <span class="n">w_prime</span> <span class="o">!=</span> <span class="n">v</span><span class="p">:</span>
<span class="c1"># removes (w,v), add (w_prime,v) and update data structures</span>
<span class="n">G</span><span class="o">.</span><span class="n">remove_edge</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">v</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">w_prime</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="n">h_partition_in</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="n">partition</span><span class="p">:</span>
<span class="n">chords</span><span class="o">.</span><span class="n">add</span><span class="p">((</span><span class="n">w</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
<span class="n">chords</span><span class="o">.</span><span class="n">discard</span><span class="p">((</span><span class="n">w_prime</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
<span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">unsat</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">w_prime</span><span class="p">)</span>
<span class="k">return</span> <span class="kc">None</span>
<span class="c1"># If neighbor switch didn't work, use unsaturated node</span>
<span class="k">return</span> <span class="n">w_prime</span>
<span class="k">def</span> <span class="nf">_directed_neighbor_switch_rev</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">w</span><span class="p">,</span> <span class="n">unsat</span><span class="p">,</span> <span class="n">h_node_residual_in</span><span class="p">,</span> <span class="n">chords</span><span class="p">,</span> <span class="n">h_partition_out</span><span class="p">,</span> <span class="n">partition</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""The reverse of directed_neighbor_switch.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : networkx directed graph</span>
<span class="sd"> graph within which the edge swap will take place.</span>
<span class="sd"> w : integer</span>
<span class="sd"> node id for which we need to perform a neighbor switch.</span>
<span class="sd"> unsat: set of integers</span>
<span class="sd"> set of node ids that have the same degree as w and are unsaturated.</span>
<span class="sd"> h_node_residual_in: dict of integers</span>
<span class="sd"> for a given node, keeps track of the remaining stubs to be added.</span>
<span class="sd"> chords: set of tuples</span>
<span class="sd"> keeps track of available positions to add edges.</span>
<span class="sd"> h_partition_out: dict of integers</span>
<span class="sd"> for a given node, keeps track of its partition id (out degree).</span>
<span class="sd"> partition: integer</span>
<span class="sd"> partition id to check if chords have to be updated.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> Same operation as directed_neighbor_switch except it handles this operation</span>
<span class="sd"> for incoming edges instead of outgoing.</span>
<span class="sd"> """</span>
<span class="n">w_prime</span> <span class="o">=</span> <span class="n">unsat</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">unsat</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">w_prime</span><span class="p">)</span>
<span class="c1"># slightly faster declaring these as variables.</span>
<span class="n">w_neighbs</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">predecessors</span><span class="p">(</span><span class="n">w</span><span class="p">))</span>
<span class="n">w_prime_neighbs</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">predecessors</span><span class="p">(</span><span class="n">w_prime</span><span class="p">))</span>
<span class="c1"># select node v, a neighbor of w, that is not connected to w_prime.</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">w_neighbs</span><span class="p">:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">w_prime_neighbs</span><span class="p">)</span> <span class="ow">and</span> <span class="n">w_prime</span> <span class="o">!=</span> <span class="n">v</span><span class="p">:</span>
<span class="c1"># removes (v,w), add (v,w_prime) and update data structures.</span>
<span class="n">G</span><span class="o">.</span><span class="n">remove_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="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_prime</span><span class="p">)</span>
<span class="k">if</span> <span class="n">h_partition_out</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="n">partition</span><span class="p">:</span>
<span class="n">chords</span><span class="o">.</span><span class="n">add</span><span class="p">((</span><span class="n">v</span><span class="p">,</span> <span class="n">w</span><span class="p">))</span>
<span class="n">chords</span><span class="o">.</span><span class="n">discard</span><span class="p">((</span><span class="n">v</span><span class="p">,</span> <span class="n">w_prime</span><span class="p">))</span>
<span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">w_prime</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">unsat</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">w_prime</span><span class="p">)</span>
<span class="k">return</span> <span class="kc">None</span>
<span class="c1"># If neighbor switch didn't work, use the unsaturated node.</span>
<span class="k">return</span> <span class="n">w_prime</span>
<div class="viewcode-block" id="directed_joint_degree_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.generators.joint_degree_seq.directed_joint_degree_graph.html#networkx.generators.joint_degree_seq.directed_joint_degree_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">directed_joint_degree_graph</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">,</span> <span class="n">out_degrees</span><span class="p">,</span> <span class="n">nkk</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">"""Generates a random simple directed graph with the joint degree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> degree_seq : list of tuples (of size 3)</span>
<span class="sd"> degree sequence contains tuples of nodes with node id, in degree and</span>
<span class="sd"> out degree.</span>
<span class="sd"> nkk : dictionary of dictionary of integers</span>
<span class="sd"> directed joint degree dictionary, for nodes of out degree k (first</span>
<span class="sd"> level of dict) and nodes of in degree l (second level of dict)</span>
<span class="sd"> describes the number of edges.</span>
<span class="sd"> seed : hashable object, optional</span>
<span class="sd"> Seed for random number generator.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> G : Graph</span>
<span class="sd"> A directed graph with the specified inputs.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> If degree_seq and nkk are not realizable as a simple directed graph.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> Similarly to the undirected version:</span>
<span class="sd"> In each iteration of the "while loop" the algorithm picks two disconnected</span>
<span class="sd"> nodes v and w, of degree k and l correspondingly, for which nkk[k][l] has</span>
<span class="sd"> not reached its target yet i.e. (for given k,l): n_edges_add < nkk[k][l].</span>
<span class="sd"> It then adds edge (v,w) and always increases the number of edges in graph G</span>
<span class="sd"> by one.</span>
<span class="sd"> The intelligence of the algorithm lies in the fact that it is always</span>
<span class="sd"> possible to add an edge between disconnected nodes v and w, for which</span>
<span class="sd"> nkk[degree(v)][degree(w)] has not reached its target, even if one or both</span>
<span class="sd"> nodes do not have free stubs. If either node v or w does not have a free</span>
<span class="sd"> stub, we perform a "neighbor switch", an edge rewiring move that releases a</span>
<span class="sd"> free stub while keeping nkk the same.</span>
<span class="sd"> The difference for the directed version lies in the fact that neighbor</span>
<span class="sd"> switches might not be able to rewire, but in these cases unsaturated nodes</span>
<span class="sd"> can be reassigned to use instead, see [1] for detailed description and</span>
<span class="sd"> proofs.</span>
<span class="sd"> The algorithm continues for E (number of edges in the graph) iterations of</span>
<span class="sd"> the "while loop", at which point all entries of the given nkk[k][l] have</span>
<span class="sd"> reached their target values and the construction is complete.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] B. Tillman, A. Markopoulou, C. T. Butts & M. Gjoka,</span>
<span class="sd"> "Construction of Directed 2K Graphs". In Proc. of KDD 2017.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> in_degrees = [0, 1, 1, 2]</span>
<span class="sd"> >>> out_degrees = [1, 1, 1, 1]</span>
<span class="sd"> >>> nkk = {1: {1: 2, 2: 2}}</span>
<span class="sd"> >>> G = nx.directed_joint_degree_graph(in_degrees, out_degrees, nkk)</span>
<span class="sd"> >>></span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_valid_directed_joint_degree</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">,</span> <span class="n">out_degrees</span><span class="p">,</span> <span class="n">nkk</span><span class="p">):</span>
<span class="n">msg</span> <span class="o">=</span> <span class="s2">"Input is not realizable as a simple graph"</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="n">msg</span><span class="p">)</span>
<span class="c1"># start with an empty directed graph.</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="c1"># for a given group, keep the list of all node ids.</span>
<span class="n">h_degree_nodelist_in</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">h_degree_nodelist_out</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># for a given group, keep the list of all unsaturated node ids.</span>
<span class="n">h_degree_nodelist_in_unsat</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">h_degree_nodelist_out_unsat</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># for a given node, keep track of the remaining stubs to be added.</span>
<span class="n">h_node_residual_out</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">h_node_residual_in</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># for a given node, keep track of the partition id.</span>
<span class="n">h_partition_out</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">h_partition_in</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># keep track of non-chords between pairs of partition ids.</span>
<span class="n">non_chords</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># populate data structures</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">in_degrees</span><span class="p">):</span>
<span class="n">idx</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">h_degree_nodelist_in</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="p">[])</span>
<span class="n">h_degree_nodelist_in_unsat</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="nb">set</span><span class="p">())</span>
<span class="n">h_degree_nodelist_in</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">h_degree_nodelist_in_unsat</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
<span class="n">h_partition_in</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">o</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">out_degrees</span><span class="p">):</span>
<span class="n">o</span> <span class="o">=</span> <span class="n">out_degrees</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">non_chords</span><span class="p">[(</span><span class="n">o</span><span class="p">,</span> <span class="n">in_degrees</span><span class="p">[</span><span class="n">idx</span><span class="p">])]</span> <span class="o">=</span> <span class="n">non_chords</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">o</span><span class="p">,</span> <span class="n">in_degrees</span><span class="p">[</span><span class="n">idx</span><span class="p">]),</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">idx</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="k">if</span> <span class="n">o</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">h_degree_nodelist_out</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="p">[])</span>
<span class="n">h_degree_nodelist_out_unsat</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="nb">set</span><span class="p">())</span>
<span class="n">h_degree_nodelist_out</span><span class="p">[</span><span class="n">o</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">h_degree_nodelist_out_unsat</span><span class="p">[</span><span class="n">o</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">o</span>
<span class="n">h_partition_out</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">o</span>
<span class="n">G</span><span class="o">.</span><span class="n">add_node</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">nk_in</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">nk_out</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">h_degree_nodelist_in</span><span class="p">:</span>
<span class="n">nk_in</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">h_degree_nodelist_in</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">h_degree_nodelist_out</span><span class="p">:</span>
<span class="n">nk_out</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">h_degree_nodelist_out</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
<span class="c1"># iterate over every degree pair (k,l) and add the number of edges given</span>
<span class="c1"># for each pair.</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">nkk</span><span class="p">:</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">nkk</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
<span class="n">n_edges_add</span> <span class="o">=</span> <span class="n">nkk</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">l</span><span class="p">]</span>
<span class="k">if</span> <span class="n">n_edges_add</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># chords contains a random set of potential edges.</span>
<span class="n">chords</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">k_len</span> <span class="o">=</span> <span class="n">nk_out</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
<span class="n">l_len</span> <span class="o">=</span> <span class="n">nk_in</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
<span class="n">chords_sample</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span>
<span class="nb">range</span><span class="p">(</span><span class="n">k_len</span> <span class="o">*</span> <span class="n">l_len</span><span class="p">),</span> <span class="n">n_edges_add</span> <span class="o">+</span> <span class="n">non_chords</span><span class="o">.</span><span class="n">get</span><span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">l</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">num</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">chords</span><span class="p">)</span> <span class="o"><</span> <span class="n">n_edges_add</span><span class="p">:</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">h_degree_nodelist_out</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">chords_sample</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">%</span> <span class="n">k_len</span><span class="p">]</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">h_degree_nodelist_in</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">chords_sample</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">//</span> <span class="n">k_len</span><span class="p">]</span>
<span class="n">num</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="n">j</span><span class="p">:</span>
<span class="n">chords</span><span class="o">.</span><span class="n">add</span><span class="p">((</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">))</span>
<span class="c1"># k_unsat and l_unsat consist of nodes of in/out degree k and l</span>
<span class="c1"># that are unsaturated i.e. those nodes that have at least one</span>
<span class="c1"># available stub</span>
<span class="n">k_unsat</span> <span class="o">=</span> <span class="n">h_degree_nodelist_out_unsat</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
<span class="n">l_unsat</span> <span class="o">=</span> <span class="n">h_degree_nodelist_in_unsat</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
<span class="k">while</span> <span class="n">n_edges_add</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
<span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">chords</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">chords</span><span class="o">.</span><span class="n">add</span><span class="p">((</span><span class="n">v</span><span class="p">,</span> <span class="n">w</span><span class="p">))</span>
<span class="c1"># if node v has no free stubs then do neighbor switch.</span>
<span class="k">if</span> <span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">_v</span> <span class="o">=</span> <span class="n">_directed_neighbor_switch</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span>
<span class="n">v</span><span class="p">,</span>
<span class="n">k_unsat</span><span class="p">,</span>
<span class="n">h_node_residual_out</span><span class="p">,</span>
<span class="n">chords</span><span class="p">,</span>
<span class="n">h_partition_in</span><span class="p">,</span>
<span class="n">l</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">_v</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_v</span>
<span class="c1"># if node w has no free stubs then do neighbor switch.</span>
<span class="k">if</span> <span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">_w</span> <span class="o">=</span> <span class="n">_directed_neighbor_switch_rev</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span>
<span class="n">w</span><span class="p">,</span>
<span class="n">l_unsat</span><span class="p">,</span>
<span class="n">h_node_residual_in</span><span class="p">,</span>
<span class="n">chords</span><span class="p">,</span>
<span class="n">h_partition_out</span><span class="p">,</span>
<span class="n">k</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">_w</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">_w</span>
<span class="c1"># add edge (v,w) and update data structures.</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="n">h_node_residual_out</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="n">h_node_residual_in</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">n_edges_add</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">chords</span><span class="o">.</span><span class="n">discard</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="k">if</span> <span class="n">h_node_residual_out</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">k_unsat</span><span class="o">.</span><span class="n">discard</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="n">h_node_residual_in</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">l_unsat</span><span class="o">.</span><span class="n">discard</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>
</pre></div>
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