htSrSSKrSSKJr S/r\"S5\R "SS9S Sj55rS rS r g) z'Distance measures approximated metrics.N)py_random_statediameterapproximate_diameter)namecU(d[R"S5eUR5S:XagUR5(a [ X5$[ X5$)uReturns 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 Examples -------- >>> G = nx.path_graph(10) # undirected graph >>> nx.diameter(G) 9 >>> G = nx.cycle_graph(3, create_using=nx.DiGraph) # directed graph >>> nx.diameter(G) 2 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)nx NetworkXErrornumber_of_nodes is_directed_two_sweep_directed_two_sweep_undirected)Gseeds e/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/approximation/distance_measures.pyrr sOD CDDa}}"1++  ))cUR[U55n[R"X5n[ U5[ U5:wa[R "S5eUGtpE[R "X5$)a0Helper function for finding a lower bound on the diameter for undirected Graphs. The idea is to pick the farthest node from a random node and return its eccentricity. ``G`` is a NetworkX undirected graph. .. note:: ``seed`` is a random.Random or numpy.random.RandomState instance zGraph not connected.)choicelistr shortest_path_lengthlenr eccentricity)rrsource distances_nodes rrrWs^[[a !F''2I 9~Q566HQ ??1 ##rcUR5nUR[U55n[R"X5n[R"X#5n[ U5n[ U5U:wd[ U5U:wa[R "S5eUGtpxUGtpy[[R"X(5[R"X 55$)aHelper 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.) reverserrr rrr maxr) rr G_reversedrforward_distancesbackward_distancesnra_1a_2s rr r qs(J [[a !F//:00D AA "c*<&=&B@AAGQ GQ rz/1H IIr)N) __doc__networkxr networkx.utils.decoratorsr__all__ _dispatchablerrr rrr,sP-5 ,-.I*/I*X$4%Jr