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<h1>Source code for networkx.algorithms.tree.mst</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Algorithms for calculating min/max spanning trees/forests.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">dataclasses</span> <span class="kn">import</span> <span class="n">dataclass</span><span class="p">,</span> <span class="n">field</span>
<span class="kn">from</span> <span class="nn">enum</span> <span class="kn">import</span> <span class="n">Enum</span>
<span class="kn">from</span> <span class="nn">heapq</span> <span class="kn">import</span> <span class="n">heappop</span><span class="p">,</span> <span class="n">heappush</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">count</span>
<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">isnan</span>
<span class="kn">from</span> <span class="nn">operator</span> <span class="kn">import</span> <span class="n">itemgetter</span>
<span class="kn">from</span> <span class="nn">queue</span> <span class="kn">import</span> <span class="n">PriorityQueue</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">UnionFind</span><span class="p">,</span> <span class="n">not_implemented_for</span><span class="p">,</span> <span class="n">py_random_state</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"minimum_spanning_edges"</span><span class="p">,</span>
<span class="s2">"maximum_spanning_edges"</span><span class="p">,</span>
<span class="s2">"minimum_spanning_tree"</span><span class="p">,</span>
<span class="s2">"maximum_spanning_tree"</span><span class="p">,</span>
<span class="s2">"random_spanning_tree"</span><span class="p">,</span>
<span class="s2">"partition_spanning_tree"</span><span class="p">,</span>
<span class="s2">"EdgePartition"</span><span class="p">,</span>
<span class="s2">"SpanningTreeIterator"</span><span class="p">,</span>
<span class="p">]</span>
<span class="k">class</span> <span class="nc">EdgePartition</span><span class="p">(</span><span class="n">Enum</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> An enum to store the state of an edge partition. The enum is written to the</span>
<span class="sd"> edges of a graph before being pasted to `kruskal_mst_edges`. Options are:</span>
<span class="sd"> - EdgePartition.OPEN</span>
<span class="sd"> - EdgePartition.INCLUDED</span>
<span class="sd"> - EdgePartition.EXCLUDED</span>
<span class="sd"> """</span>
<span class="n">OPEN</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">INCLUDED</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">EXCLUDED</span> <span class="o">=</span> <span class="mi">2</span>
<span class="nd">@not_implemented_for</span><span class="p">(</span><span class="s2">"multigraph"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">boruvka_mst_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">False</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="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Iterate over edges of a Borůvka's algorithm min/max spanning tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> The edges of `G` must have distinct weights,</span>
<span class="sd"> otherwise the edges may not form a tree.</span>
<span class="sd"> minimum : bool (default: True)</span>
<span class="sd"> Find the minimum (True) or maximum (False) spanning tree.</span>
<span class="sd"> weight : string (default: 'weight')</span>
<span class="sd"> The name of the edge attribute holding the edge weights.</span>
<span class="sd"> keys : bool (default: True)</span>
<span class="sd"> This argument is ignored since this function is not</span>
<span class="sd"> implemented for multigraphs; it exists only for consistency</span>
<span class="sd"> with the other minimum spanning tree functions.</span>
<span class="sd"> data : bool (default: True)</span>
<span class="sd"> Flag for whether to yield edge attribute dicts.</span>
<span class="sd"> If True, yield edges `(u, v, d)`, where `d` is the attribute dict.</span>
<span class="sd"> If False, yield edges `(u, v)`.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> """</span>
<span class="c1"># Initialize a forest, assuming initially that it is the discrete</span>
<span class="c1"># partition of the nodes of the graph.</span>
<span class="n">forest</span> <span class="o">=</span> <span class="n">UnionFind</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">best_edge</span><span class="p">(</span><span class="n">component</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns the optimum (minimum or maximum) edge on the edge</span>
<span class="sd"> boundary of the given set of nodes.</span>
<span class="sd"> A return value of ``None`` indicates an empty boundary.</span>
<span class="sd"> """</span>
<span class="n">sign</span> <span class="o">=</span> <span class="mi">1</span> <span class="k">if</span> <span class="n">minimum</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
<span class="n">minwt</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">"inf"</span><span class="p">)</span>
<span class="n">boundary</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">nx</span><span class="o">.</span><span class="n">edge_boundary</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">component</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="n">wt</span> <span class="o">=</span> <span class="n">e</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">sign</span>
<span class="k">if</span> <span class="n">isnan</span><span class="p">(</span><span class="n">wt</span><span class="p">):</span>
<span class="k">if</span> <span class="n">ignore_nan</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"NaN found as an edge weight. Edge </span><span class="si">{</span><span class="n">e</span><span class="si">}</span><span class="s2">"</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
<span class="k">if</span> <span class="n">wt</span> <span class="o"><</span> <span class="n">minwt</span><span class="p">:</span>
<span class="n">minwt</span> <span class="o">=</span> <span class="n">wt</span>
<span class="n">boundary</span> <span class="o">=</span> <span class="n">e</span>
<span class="k">return</span> <span class="n">boundary</span>
<span class="c1"># Determine the optimum edge in the edge boundary of each component</span>
<span class="c1"># in the forest.</span>
<span class="n">best_edges</span> <span class="o">=</span> <span class="p">(</span><span class="n">best_edge</span><span class="p">(</span><span class="n">component</span><span class="p">)</span> <span class="k">for</span> <span class="n">component</span> <span class="ow">in</span> <span class="n">forest</span><span class="o">.</span><span class="n">to_sets</span><span class="p">())</span>
<span class="n">best_edges</span> <span class="o">=</span> <span class="p">[</span><span class="n">edge</span> <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">best_edges</span> <span class="k">if</span> <span class="n">edge</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">]</span>
<span class="c1"># If each entry was ``None``, that means the graph was disconnected,</span>
<span class="c1"># so we are done generating the forest.</span>
<span class="k">while</span> <span class="n">best_edges</span><span class="p">:</span>
<span class="c1"># Determine the optimum edge in the edge boundary of each</span>
<span class="c1"># component in the forest.</span>
<span class="c1">#</span>
<span class="c1"># This must be a sequence, not an iterator. In this list, the</span>
<span class="c1"># same edge may appear twice, in different orientations (but</span>
<span class="c1"># that's okay, since a union operation will be called on the</span>
<span class="c1"># endpoints the first time it is seen, but not the second time).</span>
<span class="c1">#</span>
<span class="c1"># Any ``None`` indicates that the edge boundary for that</span>
<span class="c1"># component was empty, so that part of the forest has been</span>
<span class="c1"># completed.</span>
<span class="c1">#</span>
<span class="c1"># TODO This can be parallelized, both in the outer loop over</span>
<span class="c1"># each component in the forest and in the computation of the</span>
<span class="c1"># minimum. (Same goes for the identical lines outside the loop.)</span>
<span class="n">best_edges</span> <span class="o">=</span> <span class="p">(</span><span class="n">best_edge</span><span class="p">(</span><span class="n">component</span><span class="p">)</span> <span class="k">for</span> <span class="n">component</span> <span class="ow">in</span> <span class="n">forest</span><span class="o">.</span><span class="n">to_sets</span><span class="p">())</span>
<span class="n">best_edges</span> <span class="o">=</span> <span class="p">[</span><span class="n">edge</span> <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">best_edges</span> <span class="k">if</span> <span class="n">edge</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">]</span>
<span class="c1"># Join trees in the forest using the best edges, and yield that</span>
<span class="c1"># edge, since it is part of the spanning tree.</span>
<span class="c1">#</span>
<span class="c1"># TODO This loop can be parallelized, to an extent (the union</span>
<span class="c1"># operation must be atomic).</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">best_edges</span><span class="p">:</span>
<span class="k">if</span> <span class="n">forest</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">!=</span> <span class="n">forest</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</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="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span>
<span class="n">forest</span><span class="o">.</span><span class="n">union</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">def</span> <span class="nf">kruskal_mst_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">partition</span><span class="o">=</span><span class="kc">None</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Iterate over edge of a Kruskal's algorithm min/max spanning tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> The graph holding the tree of interest.</span>
<span class="sd"> minimum : bool (default: True)</span>
<span class="sd"> Find the minimum (True) or maximum (False) spanning tree.</span>
<span class="sd"> weight : string (default: 'weight')</span>
<span class="sd"> The name of the edge attribute holding the edge weights.</span>
<span class="sd"> keys : bool (default: True)</span>
<span class="sd"> If `G` is a multigraph, `keys` controls whether edge keys ar yielded.</span>
<span class="sd"> Otherwise `keys` is ignored.</span>
<span class="sd"> data : bool (default: True)</span>
<span class="sd"> Flag for whether to yield edge attribute dicts.</span>
<span class="sd"> If True, yield edges `(u, v, d)`, where `d` is the attribute dict.</span>
<span class="sd"> If False, yield edges `(u, v)`.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> partition : string (default: None)</span>
<span class="sd"> The name of the edge attribute holding the partition data, if it exists.</span>
<span class="sd"> Partition data is written to the edges using the `EdgePartition` enum.</span>
<span class="sd"> If a partition exists, all included edges and none of the excluded edges</span>
<span class="sd"> will appear in the final tree. Open edges may or may not be used.</span>
<span class="sd"> Yields</span>
<span class="sd"> ------</span>
<span class="sd"> edge tuple</span>
<span class="sd"> The edges as discovered by Kruskal's method. Each edge can</span>
<span class="sd"> take the following forms: `(u, v)`, `(u, v, d)` or `(u, v, k, d)`</span>
<span class="sd"> depending on the `key` and `data` parameters</span>
<span class="sd"> """</span>
<span class="n">subtrees</span> <span class="o">=</span> <span class="n">UnionFind</span><span class="p">()</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="n">edges</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">keys</span><span class="o">=</span><span class="kc">True</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="k">else</span><span class="p">:</span>
<span class="n">edges</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Sort the edges of the graph with respect to the partition data. </span>
<span class="sd"> Edges are returned in the following order:</span>
<span class="sd"> * Included edges</span>
<span class="sd"> * Open edges from smallest to largest weight</span>
<span class="sd"> * Excluded edges</span>
<span class="sd"> """</span>
<span class="n">included_edges</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">open_edges</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">e</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">wt</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">isnan</span><span class="p">(</span><span class="n">wt</span><span class="p">):</span>
<span class="k">if</span> <span class="n">ignore_nan</span><span class="p">:</span>
<span class="k">continue</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">"NaN found as an edge weight. Edge </span><span class="si">{</span><span class="n">e</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="n">edge</span> <span class="o">=</span> <span class="p">(</span><span class="n">wt</span><span class="p">,)</span> <span class="o">+</span> <span class="n">e</span>
<span class="k">if</span> <span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">partition</span><span class="p">)</span> <span class="o">==</span> <span class="n">EdgePartition</span><span class="o">.</span><span class="n">INCLUDED</span><span class="p">:</span>
<span class="n">included_edges</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">edge</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">partition</span><span class="p">)</span> <span class="o">==</span> <span class="n">EdgePartition</span><span class="o">.</span><span class="n">EXCLUDED</span><span class="p">:</span>
<span class="k">continue</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">open_edges</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">edge</span><span class="p">)</span>
<span class="k">if</span> <span class="n">minimum</span><span class="p">:</span>
<span class="n">sorted_open_edges</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">open_edges</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">itemgetter</span><span class="p">(</span><span class="mi">0</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">sorted_open_edges</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">open_edges</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">itemgetter</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">reverse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Condense the lists into one</span>
<span class="n">included_edges</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">sorted_open_edges</span><span class="p">)</span>
<span class="n">sorted_edges</span> <span class="o">=</span> <span class="n">included_edges</span>
<span class="k">del</span> <span class="n">open_edges</span><span class="p">,</span> <span class="n">sorted_open_edges</span><span class="p">,</span> <span class="n">included_edges</span>
<span class="c1"># Multigraphs need to handle edge keys in addition to edge data.</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">for</span> <span class="n">wt</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">k</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">sorted_edges</span><span class="p">:</span>
<span class="k">if</span> <span class="n">subtrees</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">!=</span> <span class="n">subtrees</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">keys</span><span class="p">:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">d</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">k</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</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="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span>
<span class="n">subtrees</span><span class="o">.</span><span class="n">union</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">for</span> <span class="n">wt</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="ow">in</span> <span class="n">sorted_edges</span><span class="p">:</span>
<span class="k">if</span> <span class="n">subtrees</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">!=</span> <span class="n">subtrees</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</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="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span>
<span class="n">subtrees</span><span class="o">.</span><span class="n">union</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">def</span> <span class="nf">prim_mst_edges</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Iterate over edges of Prim's algorithm min/max spanning tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> The graph holding the tree of interest.</span>
<span class="sd"> minimum : bool (default: True)</span>
<span class="sd"> Find the minimum (True) or maximum (False) spanning tree.</span>
<span class="sd"> weight : string (default: 'weight')</span>
<span class="sd"> The name of the edge attribute holding the edge weights.</span>
<span class="sd"> keys : bool (default: True)</span>
<span class="sd"> If `G` is a multigraph, `keys` controls whether edge keys ar yielded.</span>
<span class="sd"> Otherwise `keys` is ignored.</span>
<span class="sd"> data : bool (default: True)</span>
<span class="sd"> Flag for whether to yield edge attribute dicts.</span>
<span class="sd"> If True, yield edges `(u, v, d)`, where `d` is the attribute dict.</span>
<span class="sd"> If False, yield edges `(u, v)`.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> """</span>
<span class="n">is_multigraph</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</span><span class="p">()</span>
<span class="n">push</span> <span class="o">=</span> <span class="n">heappush</span>
<span class="n">pop</span> <span class="o">=</span> <span class="n">heappop</span>
<span class="n">nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">count</span><span class="p">()</span>
<span class="n">sign</span> <span class="o">=</span> <span class="mi">1</span> <span class="k">if</span> <span class="n">minimum</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
<span class="k">while</span> <span class="n">nodes</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">nodes</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">frontier</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">visited</span> <span class="o">=</span> <span class="p">{</span><span class="n">u</span><span class="p">}</span>
<span class="k">if</span> <span class="n">is_multigraph</span><span class="p">:</span>
<span class="k">for</span> <span class="n">v</span><span class="p">,</span> <span class="n">keydict</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">keydict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">wt</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">sign</span>
<span class="k">if</span> <span class="n">isnan</span><span class="p">(</span><span class="n">wt</span><span class="p">):</span>
<span class="k">if</span> <span class="n">ignore_nan</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"NaN found as an edge weight. Edge </span><span class="si">{</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="si">}</span><span class="s2">"</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
<span class="n">push</span><span class="p">(</span><span class="n">frontier</span><span class="p">,</span> <span class="p">(</span><span class="n">wt</span><span class="p">,</span> <span class="nb">next</span><span class="p">(</span><span class="n">c</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">k</span><span class="p">,</span> <span class="n">d</span><span class="p">))</span>
<span class="k">else</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">G</span><span class="o">.</span><span class="n">adj</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">wt</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">sign</span>
<span class="k">if</span> <span class="n">isnan</span><span class="p">(</span><span class="n">wt</span><span class="p">):</span>
<span class="k">if</span> <span class="n">ignore_nan</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"NaN found as an edge weight. Edge </span><span class="si">{</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="si">}</span><span class="s2">"</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
<span class="n">push</span><span class="p">(</span><span class="n">frontier</span><span class="p">,</span> <span class="p">(</span><span class="n">wt</span><span class="p">,</span> <span class="nb">next</span><span class="p">(</span><span class="n">c</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="k">while</span> <span class="n">nodes</span> <span class="ow">and</span> <span class="n">frontier</span><span class="p">:</span>
<span class="k">if</span> <span class="n">is_multigraph</span><span class="p">:</span>
<span class="n">W</span><span class="p">,</span> <span class="n">_</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">k</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">pop</span><span class="p">(</span><span class="n">frontier</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">W</span><span class="p">,</span> <span class="n">_</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="o">=</span> <span class="n">pop</span><span class="p">(</span><span class="n">frontier</span><span class="p">)</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">visited</span> <span class="ow">or</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
<span class="k">continue</span>
<span class="c1"># Multigraphs need to handle edge keys in addition to edge data.</span>
<span class="k">if</span> <span class="n">is_multigraph</span> <span class="ow">and</span> <span class="n">keys</span><span class="p">:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">d</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">k</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">data</span><span class="p">:</span>
<span class="k">yield</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="k">else</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span>
<span class="c1"># update frontier</span>
<span class="n">visited</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">nodes</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">is_multigraph</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span><span class="p">,</span> <span class="n">keydict</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
<span class="k">continue</span>
<span class="k">for</span> <span class="n">k2</span><span class="p">,</span> <span class="n">d2</span> <span class="ow">in</span> <span class="n">keydict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">new_weight</span> <span class="o">=</span> <span class="n">d2</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">sign</span>
<span class="n">push</span><span class="p">(</span><span class="n">frontier</span><span class="p">,</span> <span class="p">(</span><span class="n">new_weight</span><span class="p">,</span> <span class="nb">next</span><span class="p">(</span><span class="n">c</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">k2</span><span class="p">,</span> <span class="n">d2</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span><span class="p">,</span> <span class="n">d2</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span><span class="p">[</span><span class="n">v</span><span class="p">]</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">new_weight</span> <span class="o">=</span> <span class="n">d2</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">weight</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">sign</span>
<span class="n">push</span><span class="p">(</span><span class="n">frontier</span><span class="p">,</span> <span class="p">(</span><span class="n">new_weight</span><span class="p">,</span> <span class="nb">next</span><span class="p">(</span><span class="n">c</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">d2</span><span class="p">))</span>
<span class="n">ALGORITHMS</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"boruvka"</span><span class="p">:</span> <span class="n">boruvka_mst_edges</span><span class="p">,</span>
<span class="s2">"borůvka"</span><span class="p">:</span> <span class="n">boruvka_mst_edges</span><span class="p">,</span>
<span class="s2">"kruskal"</span><span class="p">:</span> <span class="n">kruskal_mst_edges</span><span class="p">,</span>
<span class="s2">"prim"</span><span class="p">:</span> <span class="n">prim_mst_edges</span><span class="p">,</span>
<span class="p">}</span>
<div class="viewcode-block" id="minimum_spanning_edges"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.minimum_spanning_edges.html#networkx.algorithms.tree.mst.minimum_spanning_edges">[docs]</a><span class="nd">@not_implemented_for</span><span class="p">(</span><span class="s2">"directed"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">minimum_spanning_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">"kruskal"</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Generate edges in a minimum spanning forest of an undirected</span>
<span class="sd"> weighted graph.</span>
<span class="sd"> A minimum spanning tree is a subgraph of the graph (a tree)</span>
<span class="sd"> with the minimum sum of edge weights. A spanning forest is a</span>
<span class="sd"> union of the spanning trees for each connected component of the graph.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : undirected Graph</span>
<span class="sd"> An undirected graph. If `G` is connected, then the algorithm finds a</span>
<span class="sd"> spanning tree. Otherwise, a spanning forest is found.</span>
<span class="sd"> algorithm : string</span>
<span class="sd"> The algorithm to use when finding a minimum spanning tree. Valid</span>
<span class="sd"> choices are 'kruskal', 'prim', or 'boruvka'. The default is 'kruskal'.</span>
<span class="sd"> weight : string</span>
<span class="sd"> Edge data key to use for weight (default 'weight').</span>
<span class="sd"> keys : bool</span>
<span class="sd"> Whether to yield edge key in multigraphs in addition to the edge.</span>
<span class="sd"> If `G` is not a multigraph, this is ignored.</span>
<span class="sd"> data : bool, optional</span>
<span class="sd"> If True yield the edge data along with the edge.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> edges : iterator</span>
<span class="sd"> An iterator over edges in a maximum spanning tree of `G`.</span>
<span class="sd"> Edges connecting nodes `u` and `v` are represented as tuples:</span>
<span class="sd"> `(u, v, k, d)` or `(u, v, k)` or `(u, v, d)` or `(u, v)`</span>
<span class="sd"> If `G` is a multigraph, `keys` indicates whether the edge key `k` will</span>
<span class="sd"> be reported in the third position in the edge tuple. `data` indicates</span>
<span class="sd"> whether the edge datadict `d` will appear at the end of the edge tuple.</span>
<span class="sd"> If `G` is not a multigraph, the tuples are `(u, v, d)` if `data` is True</span>
<span class="sd"> or `(u, v)` if `data` is False.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> from networkx.algorithms import tree</span>
<span class="sd"> Find minimum spanning edges by Kruskal's algorithm</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2)</span>
<span class="sd"> >>> mst = tree.minimum_spanning_edges(G, algorithm="kruskal", data=False)</span>
<span class="sd"> >>> edgelist = list(mst)</span>
<span class="sd"> >>> sorted(sorted(e) for e in edgelist)</span>
<span class="sd"> [[0, 1], [1, 2], [2, 3]]</span>
<span class="sd"> Find minimum spanning edges by Prim's algorithm</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2)</span>
<span class="sd"> >>> mst = tree.minimum_spanning_edges(G, algorithm="prim", data=False)</span>
<span class="sd"> >>> edgelist = list(mst)</span>
<span class="sd"> >>> sorted(sorted(e) for e in edgelist)</span>
<span class="sd"> [[0, 1], [1, 2], [2, 3]]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For Borůvka's algorithm, each edge must have a weight attribute, and</span>
<span class="sd"> each edge weight must be distinct.</span>
<span class="sd"> For the other algorithms, if the graph edges do not have a weight</span>
<span class="sd"> attribute a default weight of 1 will be used.</span>
<span class="sd"> Modified code from David Eppstein, April 2006</span>
<span class="sd"> http://www.ics.uci.edu/~eppstein/PADS/</span>
<span class="sd"> """</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">algo</span> <span class="o">=</span> <span class="n">ALGORITHMS</span><span class="p">[</span><span class="n">algorithm</span><span class="p">]</span>
<span class="k">except</span> <span class="ne">KeyError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">algorithm</span><span class="si">}</span><span class="s2"> is not a valid choice for an algorithm."</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">err</span>
<span class="k">return</span> <span class="n">algo</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="n">weight</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="n">keys</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="n">ignore_nan</span>
<span class="p">)</span></div>
<div class="viewcode-block" id="maximum_spanning_edges"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.maximum_spanning_edges.html#networkx.algorithms.tree.mst.maximum_spanning_edges">[docs]</a><span class="nd">@not_implemented_for</span><span class="p">(</span><span class="s2">"directed"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">maximum_spanning_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">"kruskal"</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Generate edges in a maximum spanning forest of an undirected</span>
<span class="sd"> weighted graph.</span>
<span class="sd"> A maximum spanning tree is a subgraph of the graph (a tree)</span>
<span class="sd"> with the maximum possible sum of edge weights. A spanning forest is a</span>
<span class="sd"> union of the spanning trees for each connected component of the graph.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : undirected Graph</span>
<span class="sd"> An undirected graph. If `G` is connected, then the algorithm finds a</span>
<span class="sd"> spanning tree. Otherwise, a spanning forest is found.</span>
<span class="sd"> algorithm : string</span>
<span class="sd"> The algorithm to use when finding a maximum spanning tree. Valid</span>
<span class="sd"> choices are 'kruskal', 'prim', or 'boruvka'. The default is 'kruskal'.</span>
<span class="sd"> weight : string</span>
<span class="sd"> Edge data key to use for weight (default 'weight').</span>
<span class="sd"> keys : bool</span>
<span class="sd"> Whether to yield edge key in multigraphs in addition to the edge.</span>
<span class="sd"> If `G` is not a multigraph, this is ignored.</span>
<span class="sd"> data : bool, optional</span>
<span class="sd"> If True yield the edge data along with the edge.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> edges : iterator</span>
<span class="sd"> An iterator over edges in a maximum spanning tree of `G`.</span>
<span class="sd"> Edges connecting nodes `u` and `v` are represented as tuples:</span>
<span class="sd"> `(u, v, k, d)` or `(u, v, k)` or `(u, v, d)` or `(u, v)`</span>
<span class="sd"> If `G` is a multigraph, `keys` indicates whether the edge key `k` will</span>
<span class="sd"> be reported in the third position in the edge tuple. `data` indicates</span>
<span class="sd"> whether the edge datadict `d` will appear at the end of the edge tuple.</span>
<span class="sd"> If `G` is not a multigraph, the tuples are `(u, v, d)` if `data` is True</span>
<span class="sd"> or `(u, v)` if `data` is False.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> from networkx.algorithms import tree</span>
<span class="sd"> Find maximum spanning edges by Kruskal's algorithm</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2)</span>
<span class="sd"> >>> mst = tree.maximum_spanning_edges(G, algorithm="kruskal", data=False)</span>
<span class="sd"> >>> edgelist = list(mst)</span>
<span class="sd"> >>> sorted(sorted(e) for e in edgelist)</span>
<span class="sd"> [[0, 1], [0, 3], [1, 2]]</span>
<span class="sd"> Find maximum spanning edges by Prim's algorithm</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2) # assign weight 2 to edge 0-3</span>
<span class="sd"> >>> mst = tree.maximum_spanning_edges(G, algorithm="prim", data=False)</span>
<span class="sd"> >>> edgelist = list(mst)</span>
<span class="sd"> >>> sorted(sorted(e) for e in edgelist)</span>
<span class="sd"> [[0, 1], [0, 3], [2, 3]]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For Borůvka's algorithm, each edge must have a weight attribute, and</span>
<span class="sd"> each edge weight must be distinct.</span>
<span class="sd"> For the other algorithms, if the graph edges do not have a weight</span>
<span class="sd"> attribute a default weight of 1 will be used.</span>
<span class="sd"> Modified code from David Eppstein, April 2006</span>
<span class="sd"> http://www.ics.uci.edu/~eppstein/PADS/</span>
<span class="sd"> """</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">algo</span> <span class="o">=</span> <span class="n">ALGORITHMS</span><span class="p">[</span><span class="n">algorithm</span><span class="p">]</span>
<span class="k">except</span> <span class="ne">KeyError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">algorithm</span><span class="si">}</span><span class="s2"> is not a valid choice for an algorithm."</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">err</span>
<span class="k">return</span> <span class="n">algo</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="n">weight</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="n">keys</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="n">ignore_nan</span>
<span class="p">)</span></div>
<div class="viewcode-block" id="minimum_spanning_tree"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.minimum_spanning_tree.html#networkx.algorithms.tree.mst.minimum_spanning_tree">[docs]</a><span class="k">def</span> <span class="nf">minimum_spanning_tree</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">"kruskal"</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a minimum spanning tree or forest on an undirected graph `G`.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : undirected graph</span>
<span class="sd"> An undirected graph. If `G` is connected, then the algorithm finds a</span>
<span class="sd"> spanning tree. Otherwise, a spanning forest is found.</span>
<span class="sd"> weight : str</span>
<span class="sd"> Data key to use for edge weights.</span>
<span class="sd"> algorithm : string</span>
<span class="sd"> The algorithm to use when finding a minimum spanning tree. Valid</span>
<span class="sd"> choices are 'kruskal', 'prim', or 'boruvka'. The default is</span>
<span class="sd"> 'kruskal'.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> A minimum spanning tree or forest.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2)</span>
<span class="sd"> >>> T = nx.minimum_spanning_tree(G)</span>
<span class="sd"> >>> sorted(T.edges(data=True))</span>
<span class="sd"> [(0, 1, {}), (1, 2, {}), (2, 3, {})]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For Borůvka's algorithm, each edge must have a weight attribute, and</span>
<span class="sd"> each edge weight must be distinct.</span>
<span class="sd"> For the other algorithms, if the graph edges do not have a weight</span>
<span class="sd"> attribute a default weight of 1 will be used.</span>
<span class="sd"> There may be more than one tree with the same minimum or maximum weight.</span>
<span class="sd"> See :mod:`networkx.tree.recognition` for more detailed definitions.</span>
<span class="sd"> Isolated nodes with self-loops are in the tree as edgeless isolated nodes.</span>
<span class="sd"> """</span>
<span class="n">edges</span> <span class="o">=</span> <span class="n">minimum_spanning_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">algorithm</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="n">ignore_nan</span>
<span class="p">)</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="vm">__class__</span><span class="p">()</span> <span class="c1"># Same graph class as G</span>
<span class="n">T</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">graph</span><span class="p">)</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="o">.</span><span class="n">items</span><span class="p">())</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
<span class="k">return</span> <span class="n">T</span></div>
<span class="k">def</span> <span class="nf">partition_spanning_tree</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">minimum</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">partition</span><span class="o">=</span><span class="s2">"partition"</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Find a spanning tree while respecting a partition of edges.</span>
<span class="sd"> Edges can be flagged as either `INLCUDED` which are required to be in the</span>
<span class="sd"> returned tree, `EXCLUDED`, which cannot be in the returned tree and `OPEN`.</span>
<span class="sd"> This is used in the SpanningTreeIterator to create new partitions following</span>
<span class="sd"> the algorithm of Sörensen and Janssens [1]_.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : undirected graph</span>
<span class="sd"> An undirected graph.</span>
<span class="sd"> minimum : bool (default: True)</span>
<span class="sd"> Determines whether the returned tree is the minimum spanning tree of</span>
<span class="sd"> the partition of the maximum one.</span>
<span class="sd"> weight : str</span>
<span class="sd"> Data key to use for edge weights.</span>
<span class="sd"> partition : str</span>
<span class="sd"> The key for the edge attribute containing the partition</span>
<span class="sd"> data on the graph. Edges can be included, excluded or open using the</span>
<span class="sd"> `EdgePartition` enum.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> A minimum spanning tree using all of the included edges in the graph and</span>
<span class="sd"> none of the excluded edges.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] G.K. Janssens, K. Sörensen, An algorithm to generate all spanning</span>
<span class="sd"> trees in order of increasing cost, Pesquisa Operacional, 2005-08,</span>
<span class="sd"> Vol. 25 (2), p. 219-229,</span>
<span class="sd"> https://www.scielo.br/j/pope/a/XHswBwRwJyrfL88dmMwYNWp/?lang=en</span>
<span class="sd"> """</span>
<span class="n">edges</span> <span class="o">=</span> <span class="n">kruskal_mst_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span>
<span class="n">minimum</span><span class="p">,</span>
<span class="n">weight</span><span class="p">,</span>
<span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="n">ignore_nan</span><span class="p">,</span>
<span class="n">partition</span><span class="o">=</span><span class="n">partition</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="vm">__class__</span><span class="p">()</span> <span class="c1"># Same graph class as G</span>
<span class="n">T</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">graph</span><span class="p">)</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="o">.</span><span class="n">items</span><span class="p">())</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
<span class="k">return</span> <span class="n">T</span>
<div class="viewcode-block" id="maximum_spanning_tree"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.maximum_spanning_tree.html#networkx.algorithms.tree.mst.maximum_spanning_tree">[docs]</a><span class="k">def</span> <span class="nf">maximum_spanning_tree</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">"kruskal"</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a maximum spanning tree or forest on an undirected graph `G`.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : undirected graph</span>
<span class="sd"> An undirected graph. If `G` is connected, then the algorithm finds a</span>
<span class="sd"> spanning tree. Otherwise, a spanning forest is found.</span>
<span class="sd"> weight : str</span>
<span class="sd"> Data key to use for edge weights.</span>
<span class="sd"> algorithm : string</span>
<span class="sd"> The algorithm to use when finding a maximum spanning tree. Valid</span>
<span class="sd"> choices are 'kruskal', 'prim', or 'boruvka'. The default is</span>
<span class="sd"> 'kruskal'.</span>
<span class="sd"> ignore_nan : bool (default: False)</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> A maximum spanning tree or forest.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.cycle_graph(4)</span>
<span class="sd"> >>> G.add_edge(0, 3, weight=2)</span>
<span class="sd"> >>> T = nx.maximum_spanning_tree(G)</span>
<span class="sd"> >>> sorted(T.edges(data=True))</span>
<span class="sd"> [(0, 1, {}), (0, 3, {'weight': 2}), (1, 2, {})]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> For Borůvka's algorithm, each edge must have a weight attribute, and</span>
<span class="sd"> each edge weight must be distinct.</span>
<span class="sd"> For the other algorithms, if the graph edges do not have a weight</span>
<span class="sd"> attribute a default weight of 1 will be used.</span>
<span class="sd"> There may be more than one tree with the same minimum or maximum weight.</span>
<span class="sd"> See :mod:`networkx.tree.recognition` for more detailed definitions.</span>
<span class="sd"> Isolated nodes with self-loops are in the tree as edgeless isolated nodes.</span>
<span class="sd"> """</span>
<span class="n">edges</span> <span class="o">=</span> <span class="n">maximum_spanning_edges</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">algorithm</span><span class="p">,</span> <span class="n">weight</span><span class="p">,</span> <span class="n">keys</span><span class="o">=</span><span class="kc">True</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="n">ignore_nan</span><span class="o">=</span><span class="n">ignore_nan</span>
<span class="p">)</span>
<span class="n">edges</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="vm">__class__</span><span class="p">()</span> <span class="c1"># Same graph class as G</span>
<span class="n">T</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">graph</span><span class="p">)</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="o">.</span><span class="n">items</span><span class="p">())</span>
<span class="n">T</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
<span class="k">return</span> <span class="n">T</span></div>
<div class="viewcode-block" id="random_spanning_tree"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.random_spanning_tree.html#networkx.algorithms.tree.mst.random_spanning_tree">[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">random_spanning_tree</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">multiplicative</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Sample a random spanning tree using the edges weights of `G`.</span>
<span class="sd"> This function supports two different methods for determining the</span>
<span class="sd"> probability of the graph. If ``multiplicative=True``, the probability</span>
<span class="sd"> is based on the product of edge weights, and if ``multiplicative=False``</span>
<span class="sd"> it is based on the sum of the edge weight. However, since it is</span>
<span class="sd"> easier to determine the total weight of all spanning trees for the</span>
<span class="sd"> multiplicative verison, that is significantly faster and should be used if</span>
<span class="sd"> possible. Additionally, setting `weight` to `None` will cause a spanning tree</span>
<span class="sd"> to be selected with uniform probability.</span>
<span class="sd"> The function uses algorithm A8 in [1]_ .</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : nx.Graph</span>
<span class="sd"> An undirected version of the original graph.</span>
<span class="sd"> weight : string</span>
<span class="sd"> The edge key for the edge attribute holding edge weight.</span>
<span class="sd"> multiplicative : bool, default=True</span>
<span class="sd"> If `True`, the probability of each tree is the product of its edge weight</span>
<span class="sd"> over the sum of the product of all the spanning trees in the graph. If</span>
<span class="sd"> `False`, the probability is the sum of its edge weight over the sum of</span>
<span class="sd"> the sum of weights for all spanning trees in the graph.</span>
<span class="sd"> seed : integer, random_state, or None (default)</span>
<span class="sd"> Indicator of random number generation state.</span>
<span class="sd"> See :ref:`Randomness<randomness>`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> nx.Graph</span>
<span class="sd"> A spanning tree using the distribution defined by the weight of the tree.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] V. Kulkarni, Generating random combinatorial objects, Journal of</span>
<span class="sd"> Algorithms, 11 (1990), pp. 185–207</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">find_node</span><span class="p">(</span><span class="n">merged_nodes</span><span class="p">,</span> <span class="n">node</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> We can think of clusters of contracted nodes as having one</span>
<span class="sd"> representative in the graph. Each node which is not in merged_nodes</span>
<span class="sd"> is still its own representative. Since a representative can be later</span>
<span class="sd"> contracted, we need to recursively search though the dict to find</span>
<span class="sd"> the final representative, but once we know it we can use path</span>
<span class="sd"> compression to speed up the access of the representative for next time.</span>
<span class="sd"> This cannot be replaced by the standard NetworkX union_find since that</span>
<span class="sd"> data structure will merge nodes with less representing nodes into the</span>
<span class="sd"> one with more representing nodes but this function requires we merge</span>
<span class="sd"> them using the order that contract_edges contracts using.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> merged_nodes : dict</span>
<span class="sd"> The dict storing the mapping from node to representative</span>
<span class="sd"> node</span>
<span class="sd"> The node whose representative we seek</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> The representative of the `node`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">merged_nodes</span><span class="p">:</span>
<span class="k">return</span> <span class="n">node</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">rep</span> <span class="o">=</span> <span class="n">find_node</span><span class="p">(</span><span class="n">merged_nodes</span><span class="p">,</span> <span class="n">merged_nodes</span><span class="p">[</span><span class="n">node</span><span class="p">])</span>
<span class="n">merged_nodes</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="n">rep</span>
<span class="k">return</span> <span class="n">rep</span>
<span class="k">def</span> <span class="nf">prepare_graph</span><span class="p">():</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> For the graph `G`, remove all edges not in the set `V` and then</span>
<span class="sd"> contract all edges in the set `U`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> A copy of `G` which has had all edges not in `V` removed and all edges</span>
<span class="sd"> in `U` contracted.</span>
<span class="sd"> """</span>
<span class="c1"># The result is a MultiGraph version of G so that parallel edges are</span>
<span class="c1"># allowed during edge contraction</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">MultiGraph</span><span class="p">(</span><span class="n">incoming_graph_data</span><span class="o">=</span><span class="n">G</span><span class="p">)</span>
<span class="c1"># Remove all edges not in V</span>
<span class="n">edges_to_remove</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">edges</span><span class="p">())</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">V</span><span class="p">)</span>
<span class="n">result</span><span class="o">.</span><span class="n">remove_edges_from</span><span class="p">(</span><span class="n">edges_to_remove</span><span class="p">)</span>
<span class="c1"># Contract all edges in U</span>
<span class="c1">#</span>
<span class="c1"># Imagine that you have two edges to contract and they share an</span>
<span class="c1"># endpoint like this:</span>
<span class="c1"># [0] ----- [1] ----- [2]</span>
<span class="c1"># If we contract (0, 1) first, the contraction function will always</span>
<span class="c1"># delete the second node it is passed so the resulting graph would be</span>
<span class="c1"># [0] ----- [2]</span>
<span class="c1"># and edge (1, 2) no longer exists but (0, 2) would need to be contracted</span>
<span class="c1"># in its place now. That is why I use the below dict as a merge-find</span>
<span class="c1"># data structure with path compression to track how the nodes are merged.</span>
<span class="n">merged_nodes</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">U</span><span class="p">:</span>
<span class="n">u_rep</span> <span class="o">=</span> <span class="n">find_node</span><span class="p">(</span><span class="n">merged_nodes</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
<span class="n">v_rep</span> <span class="o">=</span> <span class="n">find_node</span><span class="p">(</span><span class="n">merged_nodes</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
<span class="c1"># We cannot contract a node with itself</span>
<span class="k">if</span> <span class="n">u_rep</span> <span class="o">==</span> <span class="n">v_rep</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">nx</span><span class="o">.</span><span class="n">contracted_nodes</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">u_rep</span><span class="p">,</span> <span class="n">v_rep</span><span class="p">,</span> <span class="n">self_loops</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">merged_nodes</span><span class="p">[</span><span class="n">v_rep</span><span class="p">]</span> <span class="o">=</span> <span class="n">u_rep</span>
<span class="k">return</span> <span class="n">merged_nodes</span><span class="p">,</span> <span class="n">result</span>
<span class="k">def</span> <span class="nf">spanning_tree_total_weight</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Find the sum of weights of the spanning trees of `G` using the</span>
<span class="sd"> approioate `method`.</span>
<span class="sd"> This is easy if the choosen method is 'multiplicative', since we can</span>
<span class="sd"> use Kirchhoff's Tree Matrix Theorem directly. However, with the</span>
<span class="sd"> 'additive' method, this process is slightly more complex and less</span>
<span class="sd"> computatiionally efficent as we have to find the number of spanning</span>
<span class="sd"> trees which contain each possible edge in the graph.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX Graph</span>
<span class="sd"> The graph to find the total weight of all spanning trees on.</span>
<span class="sd"> weight : string</span>
<span class="sd"> The key for the weight edge attribute of the graph.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> float</span>
<span class="sd"> The sum of either the multiplicative or additive weight for all</span>
<span class="sd"> spanning trees in the graph.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">multiplicative</span><span class="p">:</span>
<span class="k">return</span> <span class="n">nx</span><span class="o">.</span><span class="n">total_spanning_tree_weight</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># There are two cases for the total spanning tree additive weight.</span>
<span class="c1"># 1. There is one edge in the graph. Then the only spanning tree is</span>
<span class="c1"># that edge itself, which will have a total weight of that edge</span>
<span class="c1"># itself.</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_edges</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="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">weight</span><span class="p">)</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()</span><span class="o">.</span><span class="fm">__next__</span><span class="p">()[</span><span class="mi">2</span><span class="p">]</span>
<span class="c1"># 2. There are more than two edges in the graph. Then, we can find the</span>
<span class="c1"># total weight of the spanning trees using the formula in the</span>
<span class="c1"># reference paper: take the weight of that edge and multiple it by</span>
<span class="c1"># the number of spanning trees which have to include that edge. This</span>
<span class="c1"># can be accomplished by contracting the edge and finding the</span>
<span class="c1"># multiplicative total spanning tree weight if the weight of each edge</span>
<span class="c1"># is assumed to be 1, which is conviently built into networkx already,</span>
<span class="c1"># by calling total_spanning_tree_weight with weight=None</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">total</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">weight</span><span class="p">):</span>
<span class="n">total</span> <span class="o">+=</span> <span class="n">w</span> <span class="o">*</span> <span class="n">nx</span><span class="o">.</span><span class="n">total_spanning_tree_weight</span><span class="p">(</span>
<span class="n">nx</span><span class="o">.</span><span class="n">contracted_edge</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge</span><span class="o">=</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">self_loops</span><span class="o">=</span><span class="kc">False</span><span class="p">),</span> <span class="kc">None</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">total</span>
<span class="n">U</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">st_cached_value</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">V</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">())</span>
<span class="n">shuffled_edges</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">edges</span><span class="p">())</span>
<span class="n">seed</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">shuffled_edges</span><span class="p">)</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">shuffled_edges</span><span class="p">:</span>
<span class="n">e_weight</span> <span class="o">=</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">weight</span><span class="p">]</span> <span class="k">if</span> <span class="n">weight</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="k">else</span> <span class="mi">1</span>
<span class="n">node_map</span><span class="p">,</span> <span class="n">prepared_G</span> <span class="o">=</span> <span class="n">prepare_graph</span><span class="p">()</span>
<span class="n">G_total_tree_weight</span> <span class="o">=</span> <span class="n">spanning_tree_total_weight</span><span class="p">(</span><span class="n">prepared_G</span><span class="p">,</span> <span class="n">weight</span><span class="p">)</span>
<span class="c1"># Add the edge to U so that we can compute the total tree weight</span>
<span class="c1"># assuming we include that edge</span>
<span class="c1"># Now, if (u, v) cannot exist in G because it is fully contracted out</span>
<span class="c1"># of existence, then it by definition cannot influence G_e's Kirchhoff</span>
<span class="c1"># value. But, we also cannot pick it.</span>
<span class="n">rep_edge</span> <span class="o">=</span> <span class="p">(</span><span class="n">find_node</span><span class="p">(</span><span class="n">node_map</span><span class="p">,</span> <span class="n">u</span><span class="p">),</span> <span class="n">find_node</span><span class="p">(</span><span class="n">node_map</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
<span class="c1"># Check to see if the 'representative edge' for the current edge is</span>
<span class="c1"># in prepared_G. If so, then we can pick it.</span>
<span class="k">if</span> <span class="n">rep_edge</span> <span class="ow">in</span> <span class="n">prepared_G</span><span class="o">.</span><span class="n">edges</span><span class="p">:</span>
<span class="n">prepared_G_e</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">contracted_edge</span><span class="p">(</span>
<span class="n">prepared_G</span><span class="p">,</span> <span class="n">edge</span><span class="o">=</span><span class="n">rep_edge</span><span class="p">,</span> <span class="n">self_loops</span><span class="o">=</span><span class="kc">False</span>
<span class="p">)</span>
<span class="n">G_e_total_tree_weight</span> <span class="o">=</span> <span class="n">spanning_tree_total_weight</span><span class="p">(</span><span class="n">prepared_G_e</span><span class="p">,</span> <span class="n">weight</span><span class="p">)</span>
<span class="k">if</span> <span class="n">multiplicative</span><span class="p">:</span>
<span class="n">threshold</span> <span class="o">=</span> <span class="n">e_weight</span> <span class="o">*</span> <span class="n">G_e_total_tree_weight</span> <span class="o">/</span> <span class="n">G_total_tree_weight</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">numerator</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">st_cached_value</span> <span class="o">+</span> <span class="n">e_weight</span>
<span class="p">)</span> <span class="o">*</span> <span class="n">nx</span><span class="o">.</span><span class="n">total_spanning_tree_weight</span><span class="p">(</span><span class="n">prepared_G_e</span><span class="p">)</span> <span class="o">+</span> <span class="n">G_e_total_tree_weight</span>
<span class="n">denominator</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">st_cached_value</span> <span class="o">*</span> <span class="n">nx</span><span class="o">.</span><span class="n">total_spanning_tree_weight</span><span class="p">(</span><span class="n">prepared_G</span><span class="p">)</span>
<span class="o">+</span> <span class="n">G_total_tree_weight</span>
<span class="p">)</span>
<span class="n">threshold</span> <span class="o">=</span> <span class="n">numerator</span> <span class="o">/</span> <span class="n">denominator</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">threshold</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">seed</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">)</span>
<span class="k">if</span> <span class="n">z</span> <span class="o">></span> <span class="n">threshold</span><span class="p">:</span>
<span class="c1"># Remove the edge from V since we did not pick it.</span>
<span class="n">V</span><span class="o">.</span><span class="n">remove</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="c1"># Add the edge to U since we picked it.</span>
<span class="n">st_cached_value</span> <span class="o">+=</span> <span class="n">e_weight</span>
<span class="n">U</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="n">v</span><span class="p">))</span>
<span class="c1"># If we decide to keep an edge, it may complete the spanning tree.</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">U</span><span class="p">)</span> <span class="o">==</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_nodes</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span>
<span class="n">spanning_tree</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">(</span><span class="n">U</span><span class="p">)</span>
<span class="k">return</span> <span class="n">spanning_tree</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Something went wrong! Only </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">U</span><span class="p">)</span><span class="si">}</span><span class="s2"> edges in the spanning tree!"</span><span class="p">)</span></div>
<div class="viewcode-block" id="SpanningTreeIterator"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.SpanningTreeIterator.html#networkx.algorithms.tree.mst.SpanningTreeIterator">[docs]</a><span class="k">class</span> <span class="nc">SpanningTreeIterator</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Iterate over all spanning trees of a graph in either increasing or</span>
<span class="sd"> decreasing cost.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This iterator uses the partition scheme from [1]_ (included edges,</span>
<span class="sd"> excluded edges and open edges) as well as a modified Kruskal's Algorithm</span>
<span class="sd"> to generate minimum spanning trees which respect the partition of edges.</span>
<span class="sd"> For spanning trees with the same weight, ties are broken arbitrarily.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] G.K. Janssens, K. Sörensen, An algorithm to generate all spanning</span>
<span class="sd"> trees in order of increasing cost, Pesquisa Operacional, 2005-08,</span>
<span class="sd"> Vol. 25 (2), p. 219-229,</span>
<span class="sd"> https://www.scielo.br/j/pope/a/XHswBwRwJyrfL88dmMwYNWp/?lang=en</span>
<span class="sd"> """</span>
<span class="nd">@dataclass</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">Partition</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> This dataclass represents a partition and stores a dict with the edge</span>
<span class="sd"> data and the weight of the minimum spanning tree of the partition dict.</span>
<span class="sd"> """</span>
<span class="n">mst_weight</span><span class="p">:</span> <span class="nb">float</span>
<span class="n">partition_dict</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">=</span> <span class="n">field</span><span class="p">(</span><span class="n">compare</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__copy__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="n">SpanningTreeIterator</span><span class="o">.</span><span class="n">Partition</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mst_weight</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_dict</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="p">)</span>
<div class="viewcode-block" id="SpanningTreeIterator.__init__"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.tree.mst.SpanningTreeIterator.html#networkx.algorithms.tree.mst.SpanningTreeIterator.__init__">[docs]</a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">,</span> <span class="n">minimum</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">ignore_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Initialize the iterator</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : nx.Graph</span>
<span class="sd"> The directed graph which we need to iterate trees over</span>
<span class="sd"> weight : String, default = "weight"</span>
<span class="sd"> The edge attribute used to store the weight of the edge</span>
<span class="sd"> minimum : bool, default = True</span>
<span class="sd"> Return the trees in increasing order while true and decreasing order</span>
<span class="sd"> while false.</span>
<span class="sd"> ignore_nan : bool, default = False</span>
<span class="sd"> If a NaN is found as an edge weight normally an exception is raised.</span>
<span class="sd"> If `ignore_nan is True` then that edge is ignored instead.</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">weight</span> <span class="o">=</span> <span class="n">weight</span>
<span class="bp">self</span><span class="o">.</span><span class="n">minimum</span> <span class="o">=</span> <span class="n">minimum</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ignore_nan</span> <span class="o">=</span> <span class="n">ignore_nan</span>
<span class="c1"># Randomly create a key for an edge attribute to hold the partition data</span>
<span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span> <span class="o">=</span> <span class="p">(</span>
<span class="s2">"SpanningTreeIterators super secret partition attribute name"</span>
<span class="p">)</span></div>
<span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> SpanningTreeIterator</span>
<span class="sd"> The iterator object for this graph</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span> <span class="o">=</span> <span class="n">PriorityQueue</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_clear_partition</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="p">)</span>
<span class="n">mst_weight</span> <span class="o">=</span> <span class="n">partition_spanning_tree</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">minimum</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ignore_nan</span>
<span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">weight</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span><span class="o">.</span><span class="n">put</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">Partition</span><span class="p">(</span><span class="n">mst_weight</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">minimum</span> <span class="k">else</span> <span class="o">-</span><span class="n">mst_weight</span><span class="p">,</span> <span class="nb">dict</span><span class="p">())</span>
<span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span>
<span class="k">def</span> <span class="fm">__next__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (multi)Graph</span>
<span class="sd"> The spanning tree of next greatest weight, which ties broken</span>
<span class="sd"> arbitrarily.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span><span class="o">.</span><span class="n">empty</span><span class="p">():</span>
<span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span>
<span class="k">raise</span> <span class="ne">StopIteration</span>
<span class="n">partition</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span><span class="o">.</span><span class="n">get</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_write_partition</span><span class="p">(</span><span class="n">partition</span><span class="p">)</span>
<span class="n">next_tree</span> <span class="o">=</span> <span class="n">partition_spanning_tree</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">minimum</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ignore_nan</span>
<span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_partition</span><span class="p">(</span><span class="n">partition</span><span class="p">,</span> <span class="n">next_tree</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_clear_partition</span><span class="p">(</span><span class="n">next_tree</span><span class="p">)</span>
<span class="k">return</span> <span class="n">next_tree</span>
<span class="k">def</span> <span class="nf">_partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">partition</span><span class="p">,</span> <span class="n">partition_tree</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Create new partitions based of the minimum spanning tree of the</span>
<span class="sd"> current minimum partition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> partition : Partition</span>
<span class="sd"> The Partition instance used to generate the current minimum spanning</span>
<span class="sd"> tree.</span>
<span class="sd"> partition_tree : nx.Graph</span>
<span class="sd"> The minimum spanning tree of the input partition.</span>
<span class="sd"> """</span>
<span class="c1"># create two new partitions with the data from the input partition dict</span>
<span class="n">p1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Partition</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">partition</span><span class="o">.</span><span class="n">partition_dict</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<span class="n">p2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Partition</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">partition</span><span class="o">.</span><span class="n">partition_dict</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">partition_tree</span><span class="o">.</span><span class="n">edges</span><span class="p">:</span>
<span class="c1"># determine if the edge was open or included</span>
<span class="k">if</span> <span class="n">e</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">partition</span><span class="o">.</span><span class="n">partition_dict</span><span class="p">:</span>
<span class="c1"># This is an open edge</span>
<span class="n">p1</span><span class="o">.</span><span class="n">partition_dict</span><span class="p">[</span><span class="n">e</span><span class="p">]</span> <span class="o">=</span> <span class="n">EdgePartition</span><span class="o">.</span><span class="n">EXCLUDED</span>
<span class="n">p2</span><span class="o">.</span><span class="n">partition_dict</span><span class="p">[</span><span class="n">e</span><span class="p">]</span> <span class="o">=</span> <span class="n">EdgePartition</span><span class="o">.</span><span class="n">INCLUDED</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_write_partition</span><span class="p">(</span><span class="n">p1</span><span class="p">)</span>
<span class="n">p1_mst</span> <span class="o">=</span> <span class="n">partition_spanning_tree</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">minimum</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">ignore_nan</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">p1_mst_weight</span> <span class="o">=</span> <span class="n">p1_mst</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">weight</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
<span class="k">if</span> <span class="n">nx</span><span class="o">.</span><span class="n">is_connected</span><span class="p">(</span><span class="n">p1_mst</span><span class="p">):</span>
<span class="n">p1</span><span class="o">.</span><span class="n">mst_weight</span> <span class="o">=</span> <span class="n">p1_mst_weight</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">minimum</span> <span class="k">else</span> <span class="o">-</span><span class="n">p1_mst_weight</span>
<span class="bp">self</span><span class="o">.</span><span class="n">partition_queue</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">p1</span><span class="o">.</span><span class="n">__copy__</span><span class="p">())</span>
<span class="n">p1</span><span class="o">.</span><span class="n">partition_dict</span> <span class="o">=</span> <span class="n">p2</span><span class="o">.</span><span class="n">partition_dict</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">_write_partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">partition</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Writes the desired partition into the graph to calculate the minimum</span>
<span class="sd"> spanning tree.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> partition : Partition</span>
<span class="sd"> A Partition dataclass describing a partition on the edges of the</span>
<span class="sd"> graph.</span>
<span class="sd"> """</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="k">if</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="ow">in</span> <span class="n">partition</span><span class="o">.</span><span class="n">partition_dict</span><span class="p">:</span>
<span class="n">d</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">]</span> <span class="o">=</span> <span class="n">partition</span><span class="o">.</span><span class="n">partition_dict</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="n">d</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">]</span> <span class="o">=</span> <span class="n">EdgePartition</span><span class="o">.</span><span class="n">OPEN</span>
<span class="k">def</span> <span class="nf">_clear_partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Removes partition data from the graph</span>
<span class="sd"> """</span>
<span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span> <span class="ow">in</span> <span class="n">d</span><span class="p">:</span>
<span class="k">del</span> <span class="n">d</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">partition_key</span><span class="p">]</span></div>
</pre></div>
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