U ?h®ã@sDdZddlZddlmZdgZedƒd dd„ƒZdd„Zd d „ZdS) z'Distance measures approximated metrics.éN)Úpy_random_stateÚdiameterécCs:|st d¡‚| ¡dkrdS| ¡r0t||ƒSt||ƒS)u¥Returns a lower bound on the diameter of the graph G. The function computes a lower bound on the diameter (i.e., the maximum eccentricity) of a directed or undirected graph G. The procedure used varies depending on the graph being directed or not. If G is an `undirected` graph, then the function uses the `2-sweep` algorithm [1]_. The main idea is to pick the farthest node from a random node and return its eccentricity. Otherwise, if G is a `directed` graph, the function uses the `2-dSweep` algorithm [2]_, The procedure starts by selecting a random source node $s$ from which it performs a forward and a backward BFS. Let $a_1$ and $a_2$ be the farthest nodes in the forward and backward cases, respectively. Then, it computes the backward eccentricity of $a_1$ using a backward BFS and the forward eccentricity of $a_2$ using a forward BFS. Finally, it returns the best lower bound between the two. In both cases, the time complexity is linear with respect to the size of G. Parameters ---------- G : NetworkX graph seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- d : integer Lower Bound on the Diameter of G Raises ------ NetworkXError If the graph is empty or If the graph is undirected and not connected or If the graph is directed and not strongly connected. See Also -------- networkx.algorithms.distance_measures.diameter References ---------- .. [1] Magnien, Clémence, Matthieu Latapy, and Michel Habib. *Fast computation of empirically tight bounds for the diameter of massive graphs.* Journal of Experimental Algorithmics (JEA), 2009. https://arxiv.org/pdf/0904.2728.pdf .. [2] Crescenzi, Pierluigi, Roberto Grossi, Leonardo Lanzi, and Andrea Marino. *On computing the diameter of real-world directed (weighted) graphs.* International Symposium on Experimental Algorithms. Springer, Berlin, Heidelberg, 2012. https://courses.cs.ut.ee/MTAT.03.238/2014_fall/uploads/Main/diameter.pdf z"Expected non-empty NetworkX graph!rr)ÚnxÚ NetworkXErrorZnumber_of_nodesZ is_directedÚ_two_sweep_directedÚ_two_sweep_undirected)ÚGÚseed©r úe/var/www/html/venv/lib/python3.8/site-packages/networkx/algorithms/approximation/distance_measures.pyr s8   cCsJ| t|ƒ¡}t ||¡}t|ƒt|ƒkr4t d¡‚|^}}t ||¡S)aLHelper function for finding a lower bound on the diameter for undirected Graphs. The idea is to pick the farthest node from a random node and return its eccentricity. ``G`` is a NetworkX undirected graph. .. note:: ``seed`` is a random.Random or numpy.random.RandomState instance zGraph not connected.)ÚchoiceÚlistrÚshortest_path_lengthÚlenrÚ eccentricity)r r ÚsourceZ distancesÚ_Únoder r r rMs    rc Cs†| ¡}| t|ƒ¡}t ||¡}t ||¡}t|ƒ}t|ƒ|ksNt|ƒ|krXt d¡‚|^}}|^}} tt ||¡t || ¡ƒS)a Helper function for finding a lower bound on the diameter for directed Graphs. It implements 2-dSweep, the directed version of the 2-sweep algorithm. The algorithm follows the following steps. 1. Select a source node $s$ at random. 2. Perform a forward BFS from $s$ to select a node $a_1$ at the maximum distance from the source, and compute $LB_1$, the backward eccentricity of $a_1$. 3. Perform a backward BFS from $s$ to select a node $a_2$ at the maximum distance from the source, and compute $LB_2$, the forward eccentricity of $a_2$. 4. Return the maximum between $LB_1$ and $LB_2$. ``G`` is a NetworkX directed graph. .. note:: ``seed`` is a random.Random or numpy.random.RandomState instance zDiGraph not strongly connected.) Úreverser rrrrrÚmaxr) r r Z G_reversedrZforward_distancesZbackward_distancesÚnrZa_1Za_2r r r rgs     r)N) Ú__doc__ZnetworkxrZnetworkx.utils.decoratorsrÚ__all__rrrr r r r Ús  C