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<h1>Source code for networkx.linalg.attrmatrix</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd"> Functions for constructing matrix-like objects from graph attributes.</span>
<span class="sd">"""</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"attr_matrix"</span><span class="p">,</span> <span class="s2">"attr_sparse_matrix"</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">_node_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a function that returns a value from G.nodes[u].</span>
<span class="sd"> We return a function expecting a node as its sole argument. Then, in the</span>
<span class="sd"> simplest scenario, the returned function will return G.nodes[u][node_attr].</span>
<span class="sd"> However, we also handle the case when `node_attr` is None or when it is a</span>
<span class="sd"> function itself.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> A NetworkX graph</span>
<span class="sd"> node_attr : {None, str, callable}</span>
<span class="sd"> Specification of how the value of the node attribute should be obtained</span>
<span class="sd"> from the node attribute dictionary.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> value : function</span>
<span class="sd"> A function expecting a node as its sole argument. The function will</span>
<span class="sd"> returns a value from G.nodes[u] that depends on `edge_attr`.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">node_attr</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">value</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
<span class="k">return</span> <span class="n">u</span>
<span class="k">elif</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">node_attr</span><span class="p">):</span>
<span class="c1"># assume it is a key for the node attribute dictionary</span>
<span class="k">def</span> <span class="nf">value</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
<span class="k">return</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">u</span><span class="p">][</span><span class="n">node_attr</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># Advanced: Allow users to specify something else.</span>
<span class="c1">#</span>
<span class="c1"># For example,</span>
<span class="c1"># node_attr = lambda u: G.nodes[u].get('size', .5) * 3</span>
<span class="c1">#</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">node_attr</span>
<span class="k">return</span> <span class="n">value</span>
<span class="k">def</span> <span class="nf">_edge_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a function that returns a value from G[u][v].</span>
<span class="sd"> Suppose there exists an edge between u and v. Then we return a function</span>
<span class="sd"> expecting u and v as arguments. For Graph and DiGraph, G[u][v] is</span>
<span class="sd"> the edge attribute dictionary, and the function (essentially) returns</span>
<span class="sd"> G[u][v][edge_attr]. However, we also handle cases when `edge_attr` is None</span>
<span class="sd"> and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]</span>
<span class="sd"> is a dictionary of all edges between u and v. In this case, the returned</span>
<span class="sd"> function sums the value of `edge_attr` for every edge between u and v.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> A NetworkX graph</span>
<span class="sd"> edge_attr : {None, str, callable}</span>
<span class="sd"> Specification of how the value of the edge attribute should be obtained</span>
<span class="sd"> from the edge attribute dictionary, G[u][v]. For multigraphs, G[u][v]</span>
<span class="sd"> is a dictionary of all the edges between u and v. This allows for</span>
<span class="sd"> special treatment of multiedges.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> value : function</span>
<span class="sd"> A function expecting two nodes as parameters. The nodes should</span>
<span class="sd"> represent the from- and to- node of an edge. The function will</span>
<span class="sd"> return a value from G[u][v] that depends on `edge_attr`.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">edge_attr</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># topological count of edges</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</span><span class="p">():</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">G</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">else</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">edge_attr</span><span class="p">):</span>
<span class="c1"># assume it is a key for the edge attribute dictionary</span>
<span class="k">if</span> <span class="n">edge_attr</span> <span class="o">==</span> <span class="s2">"weight"</span><span class="p">:</span>
<span class="c1"># provide a default value</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</span><span class="p">():</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">edge_attr</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">G</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">values</span><span class="p">())</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="n">G</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">get</span><span class="p">(</span><span class="n">edge_attr</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># otherwise, the edge attribute MUST exist for each edge</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</span><span class="p">():</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="n">edge_attr</span><span class="p">]</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">G</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">values</span><span class="p">())</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">value</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">return</span> <span class="n">G</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">edge_attr</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># Advanced: Allow users to specify something else.</span>
<span class="c1">#</span>
<span class="c1"># Alternative default value:</span>
<span class="c1"># edge_attr = lambda u,v: G[u][v].get('thickness', .5)</span>
<span class="c1">#</span>
<span class="c1"># Function on an attribute:</span>
<span class="c1"># edge_attr = lambda u,v: abs(G[u][v]['weight'])</span>
<span class="c1">#</span>
<span class="c1"># Handle Multi(Di)Graphs differently:</span>
<span class="c1"># edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])</span>
<span class="c1">#</span>
<span class="c1"># Ignore multiple edges</span>
<span class="c1"># edge_attr = lambda u,v: 1 if len(G[u][v]) else 0</span>
<span class="c1">#</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">edge_attr</span>
<span class="k">return</span> <span class="n">value</span>
<div class="viewcode-block" id="attr_matrix"><a class="viewcode-back" href="../../../reference/generated/networkx.linalg.attrmatrix.attr_matrix.html#networkx.linalg.attrmatrix.attr_matrix">[docs]</a><span class="k">def</span> <span class="nf">attr_matrix</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span>
<span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">node_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">normalized</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">rc_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">dtype</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">order</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 the attribute matrix using attributes from `G` as a numpy array.</span>
<span class="sd"> If only `G` is passed in, then the adjacency matrix is constructed.</span>
<span class="sd"> Let A be a discrete set of values for the node attribute `node_attr`. Then</span>
<span class="sd"> the elements of A represent the rows and columns of the constructed matrix.</span>
<span class="sd"> Now, iterate through every edge e=(u,v) in `G` and consider the value</span>
<span class="sd"> of the edge attribute `edge_attr`. If ua and va are the values of the</span>
<span class="sd"> node attribute `node_attr` for u and v, respectively, then the value of</span>
<span class="sd"> the edge attribute is added to the matrix element at (ua, va).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> The NetworkX graph used to construct the attribute matrix.</span>
<span class="sd"> edge_attr : str, optional</span>
<span class="sd"> Each element of the matrix represents a running total of the</span>
<span class="sd"> specified edge attribute for edges whose node attributes correspond</span>
<span class="sd"> to the rows/cols of the matrix. The attribute must be present for</span>
<span class="sd"> all edges in the graph. If no attribute is specified, then we</span>
<span class="sd"> just count the number of edges whose node attributes correspond</span>
<span class="sd"> to the matrix element.</span>
<span class="sd"> node_attr : str, optional</span>
<span class="sd"> Each row and column in the matrix represents a particular value</span>
<span class="sd"> of the node attribute. The attribute must be present for all nodes</span>
<span class="sd"> in the graph. Note, the values of this attribute should be reliably</span>
<span class="sd"> hashable. So, float values are not recommended. If no attribute is</span>
<span class="sd"> specified, then the rows and columns will be the nodes of the graph.</span>
<span class="sd"> normalized : bool, optional</span>
<span class="sd"> If True, then each row is normalized by the summation of its values.</span>
<span class="sd"> rc_order : list, optional</span>
<span class="sd"> A list of the node attribute values. This list specifies the ordering</span>
<span class="sd"> of rows and columns of the array. If no ordering is provided, then</span>
<span class="sd"> the ordering will be random (and also, a return value).</span>
<span class="sd"> Other Parameters</span>
<span class="sd"> ----------------</span>
<span class="sd"> dtype : NumPy data-type, optional</span>
<span class="sd"> A valid NumPy dtype used to initialize the array. Keep in mind certain</span>
<span class="sd"> dtypes can yield unexpected results if the array is to be normalized.</span>
<span class="sd"> The parameter is passed to numpy.zeros(). If unspecified, the NumPy</span>
<span class="sd"> default is used.</span>
<span class="sd"> order : {'C', 'F'}, optional</span>
<span class="sd"> Whether to store multidimensional data in C- or Fortran-contiguous</span>
<span class="sd"> (row- or column-wise) order in memory. This parameter is passed to</span>
<span class="sd"> numpy.zeros(). If unspecified, the NumPy default is used.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> M : 2D NumPy ndarray</span>
<span class="sd"> The attribute matrix.</span>
<span class="sd"> ordering : list</span>
<span class="sd"> If `rc_order` was specified, then only the attribute matrix is returned.</span>
<span class="sd"> However, if `rc_order` was None, then the ordering used to construct</span>
<span class="sd"> the matrix is returned as well.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> Construct an adjacency matrix:</span>
<span class="sd"> >>> G = nx.Graph()</span>
<span class="sd"> >>> G.add_edge(0, 1, thickness=1, weight=3)</span>
<span class="sd"> >>> G.add_edge(0, 2, thickness=2)</span>
<span class="sd"> >>> G.add_edge(1, 2, thickness=3)</span>
<span class="sd"> >>> nx.attr_matrix(G, rc_order=[0, 1, 2])</span>
<span class="sd"> array([[0., 1., 1.],</span>
<span class="sd"> [1., 0., 1.],</span>
<span class="sd"> [1., 1., 0.]])</span>
<span class="sd"> Alternatively, we can obtain the matrix describing edge thickness.</span>
<span class="sd"> >>> nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])</span>
<span class="sd"> array([[0., 1., 2.],</span>
<span class="sd"> [1., 0., 3.],</span>
<span class="sd"> [2., 3., 0.]])</span>
<span class="sd"> We can also color the nodes and ask for the probability distribution over</span>
<span class="sd"> all edges (u,v) describing:</span>
<span class="sd"> Pr(v has color Y | u has color X)</span>
<span class="sd"> >>> G.nodes[0]["color"] = "red"</span>
<span class="sd"> >>> G.nodes[1]["color"] = "red"</span>
<span class="sd"> >>> G.nodes[2]["color"] = "blue"</span>
<span class="sd"> >>> rc = ["red", "blue"]</span>
<span class="sd"> >>> nx.attr_matrix(G, node_attr="color", normalized=True, rc_order=rc)</span>
<span class="sd"> array([[0.33333333, 0.66666667],</span>
<span class="sd"> [1. , 0. ]])</span>
<span class="sd"> For example, the above tells us that for all edges (u,v):</span>
<span class="sd"> Pr( v is red | u is red) = 1/3</span>
<span class="sd"> Pr( v is blue | u is red) = 2/3</span>
<span class="sd"> Pr( v is red | u is blue) = 1</span>
<span class="sd"> Pr( v is blue | u is blue) = 0</span>
<span class="sd"> Finally, we can obtain the total weights listed by the node colors.</span>
<span class="sd"> >>> nx.attr_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)</span>
<span class="sd"> array([[3., 2.],</span>
<span class="sd"> [2., 0.]])</span>
<span class="sd"> Thus, the total weight over all edges (u,v) with u and v having colors:</span>
<span class="sd"> (red, red) is 3 # the sole contribution is from edge (0,1)</span>
<span class="sd"> (red, blue) is 2 # contributions from edges (0,2) and (1,2)</span>
<span class="sd"> (blue, red) is 2 # same as (red, blue) since graph is undirected</span>
<span class="sd"> (blue, blue) is 0 # there are no edges with blue endpoints</span>
<span class="sd"> """</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">edge_value</span> <span class="o">=</span> <span class="n">_edge_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">)</span>
<span class="n">node_value</span> <span class="o">=</span> <span class="n">_node_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">)</span>
<span class="k">if</span> <span class="n">rc_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ordering</span> <span class="o">=</span> <span class="nb">list</span><span class="p">({</span><span class="n">node_value</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span><span class="p">})</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">ordering</span> <span class="o">=</span> <span class="n">rc_order</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ordering</span><span class="p">)</span>
<span class="n">undirected</span> <span class="o">=</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="n">index</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">ordering</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)))</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">)</span>
<span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">nbrdict</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adjacency</span><span class="p">():</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">nbrdict</span><span class="p">:</span>
<span class="c1"># Obtain the node attribute values.</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">index</span><span class="p">[</span><span class="n">node_value</span><span class="p">(</span><span class="n">u</span><span class="p">)],</span> <span class="n">index</span><span class="p">[</span><span class="n">node_value</span><span class="p">(</span><span class="n">v</span><span class="p">)]</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
<span class="n">M</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="o">+=</span> <span class="n">edge_value</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">if</span> <span class="n">undirected</span><span class="p">:</span>
<span class="n">M</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">M</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="k">if</span> <span class="n">undirected</span><span class="p">:</span>
<span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
<span class="k">if</span> <span class="n">normalized</span><span class="p">:</span>
<span class="n">M</span> <span class="o">/=</span> <span class="n">M</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="k">if</span> <span class="n">rc_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">M</span><span class="p">,</span> <span class="n">ordering</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">M</span></div>
<div class="viewcode-block" id="attr_sparse_matrix"><a class="viewcode-back" href="../../../reference/generated/networkx.linalg.attrmatrix.attr_sparse_matrix.html#networkx.linalg.attrmatrix.attr_sparse_matrix">[docs]</a><span class="k">def</span> <span class="nf">attr_sparse_matrix</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">node_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">normalized</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">rc_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="kc">None</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a SciPy sparse array using attributes from G.</span>
<span class="sd"> If only `G` is passed in, then the adjacency matrix is constructed.</span>
<span class="sd"> Let A be a discrete set of values for the node attribute `node_attr`. Then</span>
<span class="sd"> the elements of A represent the rows and columns of the constructed matrix.</span>
<span class="sd"> Now, iterate through every edge e=(u,v) in `G` and consider the value</span>
<span class="sd"> of the edge attribute `edge_attr`. If ua and va are the values of the</span>
<span class="sd"> node attribute `node_attr` for u and v, respectively, then the value of</span>
<span class="sd"> the edge attribute is added to the matrix element at (ua, va).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> The NetworkX graph used to construct the NumPy matrix.</span>
<span class="sd"> edge_attr : str, optional</span>
<span class="sd"> Each element of the matrix represents a running total of the</span>
<span class="sd"> specified edge attribute for edges whose node attributes correspond</span>
<span class="sd"> to the rows/cols of the matirx. The attribute must be present for</span>
<span class="sd"> all edges in the graph. If no attribute is specified, then we</span>
<span class="sd"> just count the number of edges whose node attributes correspond</span>
<span class="sd"> to the matrix element.</span>
<span class="sd"> node_attr : str, optional</span>
<span class="sd"> Each row and column in the matrix represents a particular value</span>
<span class="sd"> of the node attribute. The attribute must be present for all nodes</span>
<span class="sd"> in the graph. Note, the values of this attribute should be reliably</span>
<span class="sd"> hashable. So, float values are not recommended. If no attribute is</span>
<span class="sd"> specified, then the rows and columns will be the nodes of the graph.</span>
<span class="sd"> normalized : bool, optional</span>
<span class="sd"> If True, then each row is normalized by the summation of its values.</span>
<span class="sd"> rc_order : list, optional</span>
<span class="sd"> A list of the node attribute values. This list specifies the ordering</span>
<span class="sd"> of rows and columns of the array. If no ordering is provided, then</span>
<span class="sd"> the ordering will be random (and also, a return value).</span>
<span class="sd"> Other Parameters</span>
<span class="sd"> ----------------</span>
<span class="sd"> dtype : NumPy data-type, optional</span>
<span class="sd"> A valid NumPy dtype used to initialize the array. Keep in mind certain</span>
<span class="sd"> dtypes can yield unexpected results if the array is to be normalized.</span>
<span class="sd"> The parameter is passed to numpy.zeros(). If unspecified, the NumPy</span>
<span class="sd"> default is used.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> M : SciPy sparse array</span>
<span class="sd"> The attribute matrix.</span>
<span class="sd"> ordering : list</span>
<span class="sd"> If `rc_order` was specified, then only the matrix is returned.</span>
<span class="sd"> However, if `rc_order` was None, then the ordering used to construct</span>
<span class="sd"> the matrix is returned as well.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> Construct an adjacency matrix:</span>
<span class="sd"> >>> G = nx.Graph()</span>
<span class="sd"> >>> G.add_edge(0, 1, thickness=1, weight=3)</span>
<span class="sd"> >>> G.add_edge(0, 2, thickness=2)</span>
<span class="sd"> >>> G.add_edge(1, 2, thickness=3)</span>
<span class="sd"> >>> M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2])</span>
<span class="sd"> >>> M.toarray()</span>
<span class="sd"> array([[0., 1., 1.],</span>
<span class="sd"> [1., 0., 1.],</span>
<span class="sd"> [1., 1., 0.]])</span>
<span class="sd"> Alternatively, we can obtain the matrix describing edge thickness.</span>
<span class="sd"> >>> M = nx.attr_sparse_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])</span>
<span class="sd"> >>> M.toarray()</span>
<span class="sd"> array([[0., 1., 2.],</span>
<span class="sd"> [1., 0., 3.],</span>
<span class="sd"> [2., 3., 0.]])</span>
<span class="sd"> We can also color the nodes and ask for the probability distribution over</span>
<span class="sd"> all edges (u,v) describing:</span>
<span class="sd"> Pr(v has color Y | u has color X)</span>
<span class="sd"> >>> G.nodes[0]["color"] = "red"</span>
<span class="sd"> >>> G.nodes[1]["color"] = "red"</span>
<span class="sd"> >>> G.nodes[2]["color"] = "blue"</span>
<span class="sd"> >>> rc = ["red", "blue"]</span>
<span class="sd"> >>> M = nx.attr_sparse_matrix(G, node_attr="color", normalized=True, rc_order=rc)</span>
<span class="sd"> >>> M.toarray()</span>
<span class="sd"> array([[0.33333333, 0.66666667],</span>
<span class="sd"> [1. , 0. ]])</span>
<span class="sd"> For example, the above tells us that for all edges (u,v):</span>
<span class="sd"> Pr( v is red | u is red) = 1/3</span>
<span class="sd"> Pr( v is blue | u is red) = 2/3</span>
<span class="sd"> Pr( v is red | u is blue) = 1</span>
<span class="sd"> Pr( v is blue | u is blue) = 0</span>
<span class="sd"> Finally, we can obtain the total weights listed by the node colors.</span>
<span class="sd"> >>> M = nx.attr_sparse_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)</span>
<span class="sd"> >>> M.toarray()</span>
<span class="sd"> array([[3., 2.],</span>
<span class="sd"> [2., 0.]])</span>
<span class="sd"> Thus, the total weight over all edges (u,v) with u and v having colors:</span>
<span class="sd"> (red, red) is 3 # the sole contribution is from edge (0,1)</span>
<span class="sd"> (red, blue) is 2 # contributions from edges (0,2) and (1,2)</span>
<span class="sd"> (blue, red) is 2 # same as (red, blue) since graph is undirected</span>
<span class="sd"> (blue, blue) is 0 # there are no edges with blue endpoints</span>
<span class="sd"> """</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span> <span class="k">as</span> <span class="nn">sp</span>
<span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="c1"># call as sp.sparse</span>
<span class="n">edge_value</span> <span class="o">=</span> <span class="n">_edge_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">)</span>
<span class="n">node_value</span> <span class="o">=</span> <span class="n">_node_value</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">)</span>
<span class="k">if</span> <span class="n">rc_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ordering</span> <span class="o">=</span> <span class="nb">list</span><span class="p">({</span><span class="n">node_value</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span><span class="p">})</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">ordering</span> <span class="o">=</span> <span class="n">rc_order</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ordering</span><span class="p">)</span>
<span class="n">undirected</span> <span class="o">=</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="n">index</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">ordering</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)))</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">lil_array</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">)</span>
<span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">nbrdict</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adjacency</span><span class="p">():</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">nbrdict</span><span class="p">:</span>
<span class="c1"># Obtain the node attribute values.</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">index</span><span class="p">[</span><span class="n">node_value</span><span class="p">(</span><span class="n">u</span><span class="p">)],</span> <span class="n">index</span><span class="p">[</span><span class="n">node_value</span><span class="p">(</span><span class="n">v</span><span class="p">)]</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
<span class="n">M</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="o">+=</span> <span class="n">edge_value</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">if</span> <span class="n">undirected</span><span class="p">:</span>
<span class="n">M</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">M</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="k">if</span> <span class="n">undirected</span><span class="p">:</span>
<span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
<span class="k">if</span> <span class="n">normalized</span><span class="p">:</span>
<span class="n">M</span> <span class="o">*=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">M</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span> <span class="c1"># in-place mult preserves sparse</span>
<span class="k">if</span> <span class="n">rc_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">M</span><span class="p">,</span> <span class="n">ordering</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">M</span></div>
</pre></div>
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