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<section class="sphx-glr-example-title" id="blockmodel">
<span id="sphx-glr-auto-examples-algorithms-plot-blockmodel-py"></span><h1>Blockmodel<a class="headerlink" href="#blockmodel" title="Permalink to this heading">#</a></h1>
<p>Example of creating a block model using the quotient_graph function in NX. Data
used is the Hartford, CT drug users network:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@article</span><span class="p">{</span><span class="n">weeks2002social</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="p">{</span><span class="n">Social</span> <span class="n">networks</span> <span class="n">of</span> <span class="n">drug</span> <span class="n">users</span> <span class="ow">in</span> <span class="n">high</span><span class="o">-</span><span class="n">risk</span> <span class="n">sites</span><span class="p">:</span> <span class="n">Finding</span> <span class="n">the</span> <span class="n">connections</span><span class="p">},</span>
<span class="n">url</span> <span class="o">=</span> <span class="p">{</span><span class="n">https</span><span class="p">:</span><span class="o">//</span><span class="n">doi</span><span class="o">.</span><span class="n">org</span><span class="o">/</span><span class="mf">10.1023</span><span class="o">/</span><span class="n">A</span><span class="p">:</span><span class="mi">1015457400897</span><span class="p">},</span>
<span class="n">doi</span> <span class="o">=</span> <span class="p">{</span><span class="mf">10.1023</span><span class="o">/</span><span class="n">A</span><span class="p">:</span><span class="mi">1015457400897</span><span class="p">},</span>
<span class="n">author</span><span class="o">=</span><span class="p">{</span><span class="n">Weeks</span><span class="p">,</span> <span class="n">Margaret</span> <span class="n">R</span> <span class="ow">and</span> <span class="n">Clair</span><span class="p">,</span> <span class="n">Scott</span> <span class="ow">and</span> <span class="n">Borgatti</span><span class="p">,</span> <span class="n">Stephen</span> <span class="n">P</span> <span class="ow">and</span> <span class="n">Radda</span><span class="p">,</span> <span class="n">Kim</span> <span class="ow">and</span> <span class="n">Schensul</span><span class="p">,</span> <span class="n">Jean</span> <span class="n">J</span><span class="p">},</span>
<span class="n">journal</span><span class="o">=</span><span class="p">{{</span><span class="n">AIDS</span> <span class="ow">and</span> <span class="n">Behavior</span><span class="p">}},</span>
<span class="n">volume</span><span class="o">=</span><span class="p">{</span><span class="mi">6</span><span class="p">},</span>
<span class="n">number</span><span class="o">=</span><span class="p">{</span><span class="mi">2</span><span class="p">},</span>
<span class="n">pages</span><span class="o">=</span><span class="p">{</span><span class="mi">193</span><span class="o">--</span><span class="mi">206</span><span class="p">},</span>
<span class="n">year</span><span class="o">=</span><span class="p">{</span><span class="mi">2002</span><span class="p">},</span>
<span class="n">publisher</span><span class="o">=</span><span class="p">{</span><span class="n">Springer</span><span class="p">}</span>
<span class="p">}</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_blockmodel_001.png" srcset="../../_images/sphx_glr_plot_blockmodel_001.png" alt="plot blockmodel" class = "sphx-glr-single-img"/><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/collections.html#collections.defaultdict" title="collections.defaultdict" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class"><span class="n">defaultdict</span></a>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.cluster</span> <span class="kn">import</span> <span class="n">hierarchy</span>
<span class="kn">from</span> <span class="nn">scipy.spatial</span> <span class="kn">import</span> <span class="n">distance</span>
<span class="k">def</span> <span class="nf">create_hc</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Creates hierarchical cluster of graph G from distance matrix"""</span>
<span class="n">path_length</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">all_pairs_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="n">distances</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">),</span> <span class="nb">len</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="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">path_length</span><span class="p">:</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">p</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">distances</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="o">=</span> <span class="n">d</span>
<span class="c1"># Create hierarchical cluster</span>
<span class="n">Y</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.squareform.html#scipy.spatial.distance.squareform" title="scipy.spatial.distance.squareform" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">distance</span><span class="o">.</span><span class="n">squareform</span></a><span class="p">(</span><span class="n">distances</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.complete.html#scipy.cluster.hierarchy.complete" title="scipy.cluster.hierarchy.complete" class="sphx-glr-backref-module-scipy-cluster-hierarchy sphx-glr-backref-type-py-function"><span class="n">hierarchy</span><span class="o">.</span><span class="n">complete</span></a><span class="p">(</span><span class="n">Y</span><span class="p">)</span> <span class="c1"># Creates HC using farthest point linkage</span>
<span class="c1"># This partition selection is arbitrary, for illustrive purposes</span>
<span class="n">membership</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.fcluster.html#scipy.cluster.hierarchy.fcluster" title="scipy.cluster.hierarchy.fcluster" class="sphx-glr-backref-module-scipy-cluster-hierarchy sphx-glr-backref-type-py-function"><span class="n">hierarchy</span><span class="o">.</span><span class="n">fcluster</span></a><span class="p">(</span><span class="n">Z</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="mf">1.15</span><span class="p">))</span>
<span class="c1"># Create collection of lists for blockmodel</span>
<span class="n">partition</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/collections.html#collections.defaultdict" title="collections.defaultdict" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class"><span class="n">defaultdict</span></a><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">))),</span> <span class="n">membership</span><span class="p">):</span>
<span class="n">partition</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">)</span>
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">partition</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">read_edgelist</span><span class="p">(</span><span class="s2">"hartford_drug.edgelist"</span><span class="p">)</span>
<span class="c1"># Extract largest connected component into graph H</span>
<span class="n">H</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">connected_components</span><span class="p">(</span><span class="n">G</span><span class="p">)))</span>
<span class="c1"># Makes life easier to have consecutively labeled integer nodes</span>
<span class="n">H</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">convert_node_labels_to_integers</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
<span class="c1"># Create partitions with hierarchical clustering</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">partitions</span></a> <span class="o">=</span> <span class="n">create_hc</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
<span class="c1"># Build blockmodel graph</span>
<span class="n">BM</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">quotient_graph</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">partitions</span></a><span class="p">,</span> <span class="n">relabel</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Draw original graph</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pos</span></a> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">spring_layout</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="mi">83</span><span class="p">)</span> <span class="c1"># Seed for reproducibility</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">211</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pos</span></a><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">node_size</span></a><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="c1"># Draw block model with weighted edges and nodes sized by number of internal nodes</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">node_size</span></a> <span class="o">=</span> <span class="p">[</span><span class="n">BM</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">x</span><span class="p">][</span><span class="s2">"nnodes"</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">BM</span><span class="o">.</span><span class="n">nodes</span><span class="p">()]</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">edge_width</span></a> <span class="o">=</span> <span class="p">[(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">d</span><span class="p">[</span><span class="s2">"weight"</span><span class="p">])</span> <span class="k">for</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">d</span><span class="p">)</span> <span class="ow">in</span> <span class="n">BM</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="kc">True</span><span class="p">)]</span>
<span class="c1"># Set positions to mean of positions of internal nodes from original graph</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">posBM</span></a> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a> <span class="ow">in</span> <span class="n">BM</span><span class="p">:</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xy</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pos</span></a><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">BM</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">][</span><span class="s2">"graph"</span><span class="p">]])</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">posBM</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">]</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xy</span></a><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">BM</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">posBM</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">node_size</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">node_size</span></a><span class="p">,</span> <span class="n">width</span><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">edge_width</span></a><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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