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<h1>Source code for networkx.algorithms.shortest_paths.unweighted</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Shortest path algorithms for unweighted graphs.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"bidirectional_shortest_path"</span><span class="p">,</span>
<span class="s2">"single_source_shortest_path"</span><span class="p">,</span>
<span class="s2">"single_source_shortest_path_length"</span><span class="p">,</span>
<span class="s2">"single_target_shortest_path"</span><span class="p">,</span>
<span class="s2">"single_target_shortest_path_length"</span><span class="p">,</span>
<span class="s2">"all_pairs_shortest_path"</span><span class="p">,</span>
<span class="s2">"all_pairs_shortest_path_length"</span><span class="p">,</span>
<span class="s2">"predecessor"</span><span class="p">,</span>
<span class="p">]</span>
<div class="viewcode-block" id="single_source_shortest_path_length"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.single_source_shortest_path_length.html#networkx.algorithms.shortest_paths.unweighted.single_source_shortest_path_length">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">single_source_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute the shortest path lengths from source to all reachable nodes.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> source : node</span>
<span class="sd"> Starting node for path</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth to stop the search. Only paths of length <= cutoff are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : dict</span>
<span class="sd"> Dict keyed by node to shortest path length to source.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5)</span>
<span class="sd"> >>> length = nx.single_source_shortest_path_length(G, 0)</span>
<span class="sd"> >>> length[4]</span>
<span class="sd"> 4</span>
<span class="sd"> >>> for node in length:</span>
<span class="sd"> ... print(f"{node}: {length[node]}")</span>
<span class="sd"> 0: 0</span>
<span class="sd"> 1: 1</span>
<span class="sd"> 2: 2</span>
<span class="sd"> 3: 3</span>
<span class="sd"> 4: 4</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> shortest_path_length</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">source</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Source </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s2"> is not in G"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">cutoff</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">cutoff</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">nextlevel</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
<span class="k">return</span> <span class="nb">dict</span><span class="p">(</span><span class="n">_single_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">adj</span><span class="p">,</span> <span class="n">nextlevel</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">))</span></div>
<span class="k">def</span> <span class="nf">_single_shortest_path_length</span><span class="p">(</span><span class="n">adj</span><span class="p">,</span> <span class="n">firstlevel</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Yields (node, level) in a breadth first search</span>
<span class="sd"> Shortest Path Length helper function</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> adj : dict</span>
<span class="sd"> Adjacency dict or view</span>
<span class="sd"> firstlevel : dict</span>
<span class="sd"> starting nodes, e.g. {source: 1} or {target: 1}</span>
<span class="sd"> cutoff : int or float</span>
<span class="sd"> level at which we stop the process</span>
<span class="sd"> """</span>
<span class="n">seen</span> <span class="o">=</span> <span class="p">{}</span> <span class="c1"># level (number of hops) when seen in BFS</span>
<span class="n">level</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># the current level</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">firstlevel</span><span class="p">)</span> <span class="c1"># set of nodes to check at next level</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">adj</span><span class="p">)</span>
<span class="k">while</span> <span class="n">nextlevel</span> <span class="ow">and</span> <span class="n">cutoff</span> <span class="o">>=</span> <span class="n">level</span><span class="p">:</span>
<span class="n">thislevel</span> <span class="o">=</span> <span class="n">nextlevel</span> <span class="c1"># advance to next level</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span> <span class="c1"># and start a new set (fringe)</span>
<span class="n">found</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">thislevel</span><span class="p">:</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
<span class="n">seen</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">level</span> <span class="c1"># set the level of vertex v</span>
<span class="n">found</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">yield</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">level</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">seen</span><span class="p">)</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
<span class="k">return</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">found</span><span class="p">:</span>
<span class="n">nextlevel</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">adj</span><span class="p">[</span><span class="n">v</span><span class="p">])</span>
<span class="n">level</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">del</span> <span class="n">seen</span>
<div class="viewcode-block" id="single_target_shortest_path_length"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.single_target_shortest_path_length.html#networkx.algorithms.shortest_paths.unweighted.single_target_shortest_path_length">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">single_target_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute the shortest path lengths to target from all reachable nodes.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> target : node</span>
<span class="sd"> Target node for path</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth to stop the search. Only paths of length <= cutoff are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : iterator</span>
<span class="sd"> (source, shortest path length) iterator</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5, create_using=nx.DiGraph())</span>
<span class="sd"> >>> length = dict(nx.single_target_shortest_path_length(G, 4))</span>
<span class="sd"> >>> length[0]</span>
<span class="sd"> 4</span>
<span class="sd"> >>> for node in range(5):</span>
<span class="sd"> ... print(f"{node}: {length[node]}")</span>
<span class="sd"> 0: 4</span>
<span class="sd"> 1: 3</span>
<span class="sd"> 2: 2</span>
<span class="sd"> 3: 1</span>
<span class="sd"> 4: 0</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> single_source_shortest_path_length, shortest_path_length</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">target</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Target </span><span class="si">{</span><span class="n">target</span><span class="si">}</span><span class="s2"> is not in G"</span><span class="p">)</span>
<span class="k">if</span> <span class="n">cutoff</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">cutoff</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="c1"># handle either directed or undirected</span>
<span class="n">adj</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">pred</span> <span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">()</span> <span class="k">else</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="p">{</span><span class="n">target</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
<span class="k">return</span> <span class="n">_single_shortest_path_length</span><span class="p">(</span><span class="n">adj</span><span class="p">,</span> <span class="n">nextlevel</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">)</span></div>
<div class="viewcode-block" id="all_pairs_shortest_path_length"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.all_pairs_shortest_path_length.html#networkx.algorithms.shortest_paths.unweighted.all_pairs_shortest_path_length">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">all_pairs_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Computes the shortest path lengths between all nodes in `G`.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth at which to stop the search. Only paths of length at most</span>
<span class="sd"> `cutoff` are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : iterator</span>
<span class="sd"> (source, dictionary) iterator with dictionary keyed by target and</span>
<span class="sd"> shortest path length as the key value.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The iterator returned only has reachable node pairs.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5)</span>
<span class="sd"> >>> length = dict(nx.all_pairs_shortest_path_length(G))</span>
<span class="sd"> >>> for node in [0, 1, 2, 3, 4]:</span>
<span class="sd"> ... print(f"1 - {node}: {length[1][node]}")</span>
<span class="sd"> 1 - 0: 1</span>
<span class="sd"> 1 - 1: 0</span>
<span class="sd"> 1 - 2: 1</span>
<span class="sd"> 1 - 3: 2</span>
<span class="sd"> 1 - 4: 3</span>
<span class="sd"> >>> length[3][2]</span>
<span class="sd"> 1</span>
<span class="sd"> >>> length[2][2]</span>
<span class="sd"> 0</span>
<span class="sd"> """</span>
<span class="n">length</span> <span class="o">=</span> <span class="n">single_source_shortest_path_length</span>
<span class="c1"># TODO This can be trivially parallelized.</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">yield</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="n">cutoff</span><span class="p">))</span></div>
<div class="viewcode-block" id="bidirectional_shortest_path"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.bidirectional_shortest_path.html#networkx.algorithms.shortest_paths.unweighted.bidirectional_shortest_path">[docs]</a><span class="k">def</span> <span class="nf">bidirectional_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns a list of nodes in a shortest path between source and target.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> source : node label</span>
<span class="sd"> starting node for path</span>
<span class="sd"> target : node label</span>
<span class="sd"> ending node for path</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> path: list</span>
<span class="sd"> List of nodes in a path from source to target.</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXNoPath</span>
<span class="sd"> If no path exists between source and target.</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> shortest_path</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This algorithm is used by shortest_path(G, source, target).</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">source</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span> <span class="ow">or</span> <span class="n">target</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"Either source </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s2"> or target </span><span class="si">{</span><span class="n">target</span><span class="si">}</span><span class="s2"> is not in G"</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
<span class="c1"># call helper to do the real work</span>
<span class="n">results</span> <span class="o">=</span> <span class="n">_bidirectional_pred_succ</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">pred</span><span class="p">,</span> <span class="n">succ</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">results</span>
<span class="c1"># build path from pred+w+succ</span>
<span class="n">path</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># from source to w</span>
<span class="k">while</span> <span class="n">w</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">pred</span><span class="p">[</span><span class="n">w</span><span class="p">]</span>
<span class="n">path</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
<span class="c1"># from w to target</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">succ</span><span class="p">[</span><span class="n">path</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<span class="k">while</span> <span class="n">w</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">succ</span><span class="p">[</span><span class="n">w</span><span class="p">]</span>
<span class="k">return</span> <span class="n">path</span></div>
<span class="k">def</span> <span class="nf">_bidirectional_pred_succ</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Bidirectional shortest path helper.</span>
<span class="sd"> Returns (pred, succ, w) where</span>
<span class="sd"> pred is a dictionary of predecessors from w to the source, and</span>
<span class="sd"> succ is a dictionary of successors from w to the target.</span>
<span class="sd"> """</span>
<span class="c1"># does BFS from both source and target and meets in the middle</span>
<span class="k">if</span> <span class="n">target</span> <span class="o">==</span> <span class="n">source</span><span class="p">:</span>
<span class="k">return</span> <span class="p">({</span><span class="n">target</span><span class="p">:</span> <span class="kc">None</span><span class="p">},</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="kc">None</span><span class="p">},</span> <span class="n">source</span><span class="p">)</span>
<span class="c1"># handle either directed or undirected</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span>
<span class="n">Gpred</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">pred</span>
<span class="n">Gsucc</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">succ</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">Gpred</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span>
<span class="n">Gsucc</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span>
<span class="c1"># predecesssor and successors in search</span>
<span class="n">pred</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="kc">None</span><span class="p">}</span>
<span class="n">succ</span> <span class="o">=</span> <span class="p">{</span><span class="n">target</span><span class="p">:</span> <span class="kc">None</span><span class="p">}</span>
<span class="c1"># initialize fringes, start with forward</span>
<span class="n">forward_fringe</span> <span class="o">=</span> <span class="p">[</span><span class="n">source</span><span class="p">]</span>
<span class="n">reverse_fringe</span> <span class="o">=</span> <span class="p">[</span><span class="n">target</span><span class="p">]</span>
<span class="k">while</span> <span class="n">forward_fringe</span> <span class="ow">and</span> <span class="n">reverse_fringe</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">forward_fringe</span><span class="p">)</span> <span class="o"><=</span> <span class="nb">len</span><span class="p">(</span><span class="n">reverse_fringe</span><span class="p">):</span>
<span class="n">this_level</span> <span class="o">=</span> <span class="n">forward_fringe</span>
<span class="n">forward_fringe</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">this_level</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">Gsucc</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">pred</span><span class="p">:</span>
<span class="n">forward_fringe</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">pred</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span> <span class="c1"># path found</span>
<span class="k">return</span> <span class="n">pred</span><span class="p">,</span> <span class="n">succ</span><span class="p">,</span> <span class="n">w</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">this_level</span> <span class="o">=</span> <span class="n">reverse_fringe</span>
<span class="n">reverse_fringe</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">this_level</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">Gpred</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span>
<span class="n">succ</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
<span class="n">reverse_fringe</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">pred</span><span class="p">:</span> <span class="c1"># found path</span>
<span class="k">return</span> <span class="n">pred</span><span class="p">,</span> <span class="n">succ</span><span class="p">,</span> <span class="n">w</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXNoPath</span><span class="p">(</span><span class="sa">f</span><span class="s2">"No path between </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s2"> and </span><span class="si">{</span><span class="n">target</span><span class="si">}</span><span class="s2">."</span><span class="p">)</span>
<div class="viewcode-block" id="single_source_shortest_path"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.single_source_shortest_path.html#networkx.algorithms.shortest_paths.unweighted.single_source_shortest_path">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">single_source_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute shortest path between source</span>
<span class="sd"> and all other nodes reachable from source.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> source : node label</span>
<span class="sd"> Starting node for path</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth to stop the search. Only paths of length <= cutoff are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : dictionary</span>
<span class="sd"> Dictionary, keyed by target, of shortest paths.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5)</span>
<span class="sd"> >>> path = nx.single_source_shortest_path(G, 0)</span>
<span class="sd"> >>> path[4]</span>
<span class="sd"> [0, 1, 2, 3, 4]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The shortest path is not necessarily unique. So there can be multiple</span>
<span class="sd"> paths between the source and each target node, all of which have the</span>
<span class="sd"> same 'shortest' length. For each target node, this function returns</span>
<span class="sd"> only one of those paths.</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> shortest_path</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">source</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Source </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s2"> not in G"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">join</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">):</span>
<span class="k">return</span> <span class="n">p1</span> <span class="o">+</span> <span class="n">p2</span>
<span class="k">if</span> <span class="n">cutoff</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">cutoff</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">nextlevel</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span> <span class="c1"># list of nodes to check at next level</span>
<span class="n">paths</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="p">[</span><span class="n">source</span><span class="p">]}</span> <span class="c1"># paths dictionary (paths to key from source)</span>
<span class="k">return</span> <span class="nb">dict</span><span class="p">(</span><span class="n">_single_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">adj</span><span class="p">,</span> <span class="n">nextlevel</span><span class="p">,</span> <span class="n">paths</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">,</span> <span class="n">join</span><span class="p">))</span></div>
<span class="k">def</span> <span class="nf">_single_shortest_path</span><span class="p">(</span><span class="n">adj</span><span class="p">,</span> <span class="n">firstlevel</span><span class="p">,</span> <span class="n">paths</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">,</span> <span class="n">join</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns shortest paths</span>
<span class="sd"> Shortest Path helper function</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> adj : dict</span>
<span class="sd"> Adjacency dict or view</span>
<span class="sd"> firstlevel : dict</span>
<span class="sd"> starting nodes, e.g. {source: 1} or {target: 1}</span>
<span class="sd"> paths : dict</span>
<span class="sd"> paths for starting nodes, e.g. {source: [source]}</span>
<span class="sd"> cutoff : int or float</span>
<span class="sd"> level at which we stop the process</span>
<span class="sd"> join : function</span>
<span class="sd"> function to construct a path from two partial paths. Requires two</span>
<span class="sd"> list inputs `p1` and `p2`, and returns a list. Usually returns</span>
<span class="sd"> `p1 + p2` (forward from source) or `p2 + p1` (backward from target)</span>
<span class="sd"> """</span>
<span class="n">level</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># the current level</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="n">firstlevel</span>
<span class="k">while</span> <span class="n">nextlevel</span> <span class="ow">and</span> <span class="n">cutoff</span> <span class="o">></span> <span class="n">level</span><span class="p">:</span>
<span class="n">thislevel</span> <span class="o">=</span> <span class="n">nextlevel</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">thislevel</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">adj</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">paths</span><span class="p">:</span>
<span class="n">paths</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="n">join</span><span class="p">(</span><span class="n">paths</span><span class="p">[</span><span class="n">v</span><span class="p">],</span> <span class="p">[</span><span class="n">w</span><span class="p">])</span>
<span class="n">nextlevel</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">level</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">paths</span>
<div class="viewcode-block" id="single_target_shortest_path"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.single_target_shortest_path.html#networkx.algorithms.shortest_paths.unweighted.single_target_shortest_path">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">single_target_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute shortest path to target from all nodes that reach target.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> target : node label</span>
<span class="sd"> Target node for path</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth to stop the search. Only paths of length <= cutoff are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : dictionary</span>
<span class="sd"> Dictionary, keyed by target, of shortest paths.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5, create_using=nx.DiGraph())</span>
<span class="sd"> >>> path = nx.single_target_shortest_path(G, 4)</span>
<span class="sd"> >>> path[0]</span>
<span class="sd"> [0, 1, 2, 3, 4]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The shortest path is not necessarily unique. So there can be multiple</span>
<span class="sd"> paths between the source and each target node, all of which have the</span>
<span class="sd"> same 'shortest' length. For each target node, this function returns</span>
<span class="sd"> only one of those paths.</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> shortest_path, single_source_shortest_path</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">target</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Target </span><span class="si">{</span><span class="n">target</span><span class="si">}</span><span class="s2"> not in G"</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">join</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">):</span>
<span class="k">return</span> <span class="n">p2</span> <span class="o">+</span> <span class="n">p1</span>
<span class="c1"># handle undirected graphs</span>
<span class="n">adj</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">pred</span> <span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">()</span> <span class="k">else</span> <span class="n">G</span><span class="o">.</span><span class="n">adj</span>
<span class="k">if</span> <span class="n">cutoff</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">cutoff</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">nextlevel</span> <span class="o">=</span> <span class="p">{</span><span class="n">target</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span> <span class="c1"># list of nodes to check at next level</span>
<span class="n">paths</span> <span class="o">=</span> <span class="p">{</span><span class="n">target</span><span class="p">:</span> <span class="p">[</span><span class="n">target</span><span class="p">]}</span> <span class="c1"># paths dictionary (paths to key from source)</span>
<span class="k">return</span> <span class="nb">dict</span><span class="p">(</span><span class="n">_single_shortest_path</span><span class="p">(</span><span class="n">adj</span><span class="p">,</span> <span class="n">nextlevel</span><span class="p">,</span> <span class="n">paths</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">,</span> <span class="n">join</span><span class="p">))</span></div>
<div class="viewcode-block" id="all_pairs_shortest_path"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.all_pairs_shortest_path.html#networkx.algorithms.shortest_paths.unweighted.all_pairs_shortest_path">[docs]</a><span class="nd">@nx</span><span class="o">.</span><span class="n">_dispatch</span>
<span class="k">def</span> <span class="nf">all_pairs_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute shortest paths between all nodes.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth at which to stop the search. Only paths of length at most</span>
<span class="sd"> `cutoff` are returned.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lengths : dictionary</span>
<span class="sd"> Dictionary, keyed by source and target, of shortest paths.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(5)</span>
<span class="sd"> >>> path = dict(nx.all_pairs_shortest_path(G))</span>
<span class="sd"> >>> print(path[0][4])</span>
<span class="sd"> [0, 1, 2, 3, 4]</span>
<span class="sd"> See Also</span>
<span class="sd"> --------</span>
<span class="sd"> floyd_warshall</span>
<span class="sd"> """</span>
<span class="c1"># TODO This can be trivially parallelized.</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">yield</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">single_source_shortest_path</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="n">cutoff</span><span class="p">))</span></div>
<div class="viewcode-block" id="predecessor"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.shortest_paths.unweighted.predecessor.html#networkx.algorithms.shortest_paths.unweighted.predecessor">[docs]</a><span class="k">def</span> <span class="nf">predecessor</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">cutoff</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">return_seen</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Returns dict of predecessors for the path from source to all nodes in G.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> source : node label</span>
<span class="sd"> Starting node for path</span>
<span class="sd"> target : node label, optional</span>
<span class="sd"> Ending node for path. If provided only predecessors between</span>
<span class="sd"> source and target are returned</span>
<span class="sd"> cutoff : integer, optional</span>
<span class="sd"> Depth to stop the search. Only paths of length <= cutoff are returned.</span>
<span class="sd"> return_seen : bool, optional (default=None)</span>
<span class="sd"> Whether to return a dictionary, keyed by node, of the level (number of</span>
<span class="sd"> hops) to reach the node (as seen during breadth-first-search).</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> pred : dictionary</span>
<span class="sd"> Dictionary, keyed by node, of predecessors in the shortest path.</span>
<span class="sd"> (pred, seen): tuple of dictionaries</span>
<span class="sd"> If `return_seen` argument is set to `True`, then a tuple of dictionaries</span>
<span class="sd"> is returned. The first element is the dictionary, keyed by node, of</span>
<span class="sd"> predecessors in the shortest path. The second element is the dictionary,</span>
<span class="sd"> keyed by node, of the level (number of hops) to reach the node (as seen</span>
<span class="sd"> during breadth-first-search).</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.path_graph(4)</span>
<span class="sd"> >>> list(G)</span>
<span class="sd"> [0, 1, 2, 3]</span>
<span class="sd"> >>> nx.predecessor(G, 0)</span>
<span class="sd"> {0: [], 1: [0], 2: [1], 3: [2]}</span>
<span class="sd"> >>> nx.predecessor(G, 0, return_seen=True)</span>
<span class="sd"> ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3})</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">source</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NodeNotFound</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Source </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s2"> not in G"</span><span class="p">)</span>
<span class="n">level</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># the current level</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="p">[</span><span class="n">source</span><span class="p">]</span> <span class="c1"># list of nodes to check at next level</span>
<span class="n">seen</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="n">level</span><span class="p">}</span> <span class="c1"># level (number of hops) when seen in BFS</span>
<span class="n">pred</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">:</span> <span class="p">[]}</span> <span class="c1"># predecessor dictionary</span>
<span class="k">while</span> <span class="n">nextlevel</span><span class="p">:</span>
<span class="n">level</span> <span class="o">=</span> <span class="n">level</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">thislevel</span> <span class="o">=</span> <span class="n">nextlevel</span>
<span class="n">nextlevel</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">thislevel</span><span class="p">:</span>
<span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
<span class="n">pred</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span><span class="p">]</span>
<span class="n">seen</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">=</span> <span class="n">level</span>
<span class="n">nextlevel</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">seen</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="o">==</span> <span class="n">level</span><span class="p">:</span> <span class="c1"># add v to predecessor list if it</span>
<span class="n">pred</span><span class="p">[</span><span class="n">w</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="c1"># is at the correct level</span>
<span class="k">if</span> <span class="n">cutoff</span> <span class="ow">and</span> <span class="n">cutoff</span> <span class="o"><=</span> <span class="n">level</span><span class="p">:</span>
<span class="k">break</span>
<span class="k">if</span> <span class="n">target</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">if</span> <span class="n">return_seen</span><span class="p">:</span>
<span class="k">if</span> <span class="n">target</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">pred</span><span class="p">:</span>
<span class="k">return</span> <span class="p">([],</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># No predecessor</span>
<span class="k">return</span> <span class="p">(</span><span class="n">pred</span><span class="p">[</span><span class="n">target</span><span class="p">],</span> <span class="n">seen</span><span class="p">[</span><span class="n">target</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">target</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">pred</span><span class="p">:</span>
<span class="k">return</span> <span class="p">[]</span> <span class="c1"># No predecessor</span>
<span class="k">return</span> <span class="n">pred</span><span class="p">[</span><span class="n">target</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">return_seen</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">seen</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">pred</span></div>
</pre></div>
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