shF8SrSSKrSSKJr SSKrSSKJr SSKJ r J r J r J r /SQr \ "S5\R"SSS 9SS j55r\ "S5\R"SSS 9SS j55r\ "S 5\R"SSS 9SS j55r\ "S5\R"SSS 9SSj55r\ "S5\R"SSS 9SSj55r\R"SSS 9SSj5r\ "S5SSj5r\ "S5SSj5rg)zd Generators for some directed graphs, including growing network (GN) graphs and scale-free graphs. N)Counter) empty_graph)discrete_sequencenp_random_statepy_random_stateweighted_choice)gn_graph gnc_graph gnr_graphrandom_k_out_graphscale_free_graphT)graphs returns_graphc[SU[RS9nUR5(d[R"S5eUcSnUS:XaU$UR SS5 SS/n[ SU5HUnUVs/sH oq"U5PM nn[SXS9Sn UR Xi5 URS5 XY==S- ss'MW U$s snf)aReturns the growing network (GN) digraph with `n` nodes. The GN graph is built by adding nodes one at a time with a link to one previously added node. The target node for the link is chosen with probability based on degree. The default attachment kernel is a linear function of the degree of a node. The graph is always a (directed) tree. Parameters ---------- n : int The number of nodes for the generated graph. kernel : function The attachment kernel. create_using : NetworkX graph constructor, optional (default DiGraph) Graph type to create. If graph instance, then cleared before populated. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Examples -------- To create the undirected GN graph, use the :meth:`~DiGraph.to_directed` method:: >>> D = nx.gn_graph(10) # the GN graph >>> G = D.to_undirected() # the undirected version To specify an attachment kernel, use the `kernel` keyword argument:: >>> D = nx.gn_graph(10, kernel=lambda x: x**1.5) # A_k = k^1.5 References ---------- .. [1] P. L. Krapivsky and S. Redner, Organization of Growing Random Networks, Phys. Rev. E, 63, 066123, 2001. default+create_using must indicate a Directed GraphcU$N)xs p/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/networkx/generators/directed.pykernelgn_graph..kernelLsHr) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingr Gdssourceddisttargets rr r sT A|RZZ8A ==??LMM ~  AvJJq! QB1+#%&2aq 2&"14CAF 6" !  a  H 's<Ccr[SU[RS9nUR5(d[R"S5eUS:XaU$[ SU5HZnUR SU5nUR5U:a US:wa[URU55nURXV5 M\ U$)azReturns the growing network with redirection (GNR) digraph with `n` nodes and redirection probability `p`. The GNR graph is built by adding nodes one at a time with a link to one previously added node. The previous target node is chosen uniformly at random. With probability `p` the link is instead "redirected" to the successor node of the target. The graph is always a (directed) tree. Parameters ---------- n : int The number of nodes for the generated graph. p : float The redirection probability. create_using : NetworkX graph constructor, optional (default DiGraph) Graph type to create. If graph instance, then cleared before populated. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Examples -------- To create the undirected GNR graph, use the :meth:`~DiGraph.to_directed` method:: >>> D = nx.gnr_graph(10, 0.5) # the GNR graph >>> G = D.to_undirected() # the undirected version References ---------- .. [1] P. L. Krapivsky and S. Redner, Organization of Growing Random Networks, Phys. Rev. E, 63, 066123, 2001. rrrr) rr!r"r#r$r& randrangerandomnext successorsr%)r(pr)r r*r,r/s rr r `sN A|RZZ8A ==??LMMAv1+6* ;;=1 1!,,v./F 6"  Hrrc\[SU[RS9nUR5(d[R"S5eUS:XaU$[ SU5HOnUR SU5nURU5HnURXF5 M URXE5 MQ U$)aReturns the growing network with copying (GNC) digraph with `n` nodes. The GNC graph is built by adding nodes one at a time with a link to one previously added node (chosen uniformly at random) and to all of that node's successors. Parameters ---------- n : int The number of nodes for the generated graph. create_using : NetworkX graph constructor, optional (default DiGraph) Graph type to create. If graph instance, then cleared before populated. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. References ---------- .. [1] P. L. Krapivsky and S. Redner, Network Growth by Copying, Phys. Rev. E, 71, 036118, 2005k.}, rrrr) rr!r"r#r$r&r1r4r%)r(r)r r*r,r/succs rr r s2 A|RZZ8A ==??LMMAv1+6*LL(D JJv $) 6"  Hrc^U4SjnUbI[US5(a8[U[R5(d[R"S5eUn O[R"/SQ5n US::a [ S5eUS::a [ S5eUS::a [ S5e[ X-U-S - 5S :a [ S 5eUS:a [ S 5eUS:a [ S 5e[SU R55/5n [SU R55/5n [U R55n U Vs/sH&n[U[R5(dM$UPM( n n[U 5S:a[SU 55S-nOSn[U 5W:aTR!5nX:a"UnUS- nU R#U5 U"XU5nO`. initial_graph : MultiDiGraph instance, optional Build the scale-free graph starting from this initial MultiDiGraph, if provided. Returns ------- MultiDiGraph Examples -------- Create a scale-free graph on one hundred nodes:: >>> G = nx.scale_free_graph(100) Notes ----- The sum of `alpha`, `beta`, and `gamma` must be 1. References ---------- .. [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan, Directed scale-free graphs, Proceedings of the fourteenth annual ACM-SIAM Symposium on Discrete Algorithms, 132--139, 2003. c>US:aC[U5U-nX3[U5-- nTR5U:aTRU5$TRU5$)Nr)lenr2choice) candidates node_listdeltabias_sump_deltar s r _choose_node&scale_free_graph.._choose_nodesU 199~-HS_"<=G{{}w&{{9--{{:&&r_adjz%initial_graph must be a MultiDiGraph.))rr)rr)rrrzalpha must be > 0.zbeta must be > 0.zgamma must be > 0.g?g& .>zalpha+beta+gamma must equal 1.zdelta_in must be >= 0.zdelta_out must be >= 0.c30# UH upX!/-v M g7frr.0idxcounts r #scale_free_graph..s =n eemnc30# UH upX!/-v M g7frrrFs rrJrKs numeric_nodescursorrvws ` rr r sC|' W]F%C%C-99""#JK K  OO4 5 z-.. qy,-- z-.. 5<% # %&$.9::!|1221}233 =alln =r BB >-JQ MK =A8-881< a&1* KKM 9A aKF   Q RH5A  RI6ARH5A RI6AA aKF   Q  1a !  ! I a&1*L H]Ls #I!)I!c*^^^^ U(a[R"5nUUU4SjnO[R"5nUUU4Sjn[R"X5n[ U5nUH%m UR U 4SjU"T U555 M' U$)aReturns a random `k`-out graph with uniform attachment. A random `k`-out graph with uniform attachment is a multidigraph generated by the following algorithm. For each node *u*, choose `k` nodes *v* uniformly at random (with replacement). Add a directed edge joining *u* to *v*. Parameters ---------- n : int The number of nodes in the returned graph. k : int The out-degree of each node in the returned graph. self_loops : bool If True, self-loops are allowed when generating the graph. with_replacement : bool If True, neighbors are chosen with replacement and the returned graph will be a directed multigraph. Otherwise, neighbors are chosen without replacement and the returned graph will be a directed graph. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- NetworkX graph A `k`-out-regular directed graph generated according to the above algorithm. It will be a multigraph if and only if `with_replacement` is True. Raises ------ ValueError If `with_replacement` is False and `k` is greater than `n`. See also -------- random_k_out_graph Notes ----- The return digraph or multidigraph may not be strongly connected, or even weakly connected. If `with_replacement` is True, this function is similar to :func:`random_k_out_graph`, if that function had parameter `alpha` set to positive infinity. cL>^T(dTU1- mUU4Sj[T55$)Nc3X># UHnTR[T55v M! g7fr)r<rY)rGirZr s rrJ=random_uniform_k_out_graph..sample..s!?hDKKU ,,hs'*)r&rirZkr self_loopss `rsample*random_uniform_k_out_graph..samples  ?eAh? ?rcR>T(dX1- nTR[U5T5$r)rtrYrqs rrtrus$ ;;tE{A. .rc3,># UH nTU4v M g7frr)rGrius rrJ-random_uniform_k_out_graph..s:)9A!Q)9s)r!rSr"rsetadd_edges_from) r(rrrswith_replacementr r)rtr*rZrxs `` ` @rrandom_uniform_k_out_graphr}Usvt(  @ @ zz|  / q'A FE  :5)9:: HrczUS:a [S5e[XX#U5$![a [XX#U5s$f=f)aW Returns a random `k`-out graph with preferential attachment. .. versionchanged:: 3.5 Different implementations will be used based on whether NumPy is available. See Notes for details. A random `k`-out graph with preferential attachment is a multidigraph generated by the following algorithm. 1. Begin with an empty digraph, and initially set each node to have weight `alpha`. 2. Choose a node `u` with out-degree less than `k` uniformly at random. 3. Choose a node `v` from with probability proportional to its weight. 4. Add a directed edge from `u` to `v`, and increase the weight of `v` by one. 5. If each node has out-degree `k`, halt, otherwise repeat from step 2. For more information on this model of random graph, see [1]_. Parameters ---------- n : int The number of nodes in the returned graph. k : int The out-degree of each node in the returned graph. alpha : float A positive :class:`float` representing the initial weight of each vertex. A higher number means that in step 3 above, nodes will be chosen more like a true uniformly random sample, and a lower number means that nodes are more likely to be chosen as their in-degree increases. If this parameter is not positive, a :exc:`ValueError` is raised. self_loops : bool If True, self-loops are allowed when generating the graph. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- :class:`~networkx.classes.MultiDiGraph` A `k`-out-regular multidigraph generated according to the above algorithm. Raises ------ ValueError If `alpha` is not positive. Notes ----- The returned multidigraph may not be strongly connected, or even weakly connected. `random_k_out_graph` has two implementations: an array-based formulation that uses `numpy` (``_random_k_out_graph_numpy``), and a pure-Python implementation (``_random_k_out_graph_python``). The NumPy implementation is more performant, especially for large `n`, and is therefore used by default. If NumPy is not installed in the environment, then the pure Python implementation is executed. However, you can explicitly control which implementation is executed by directly calling the corresponding function:: # Use numpy if available, else Python nx.random_k_out_graph(1000, 5, alpha=1) # Use the numpy-based implementation (raises ImportError if numpy not installed) nx.generators.directed._random_k_out_graph_numpy(1000, 5, alpha=1) # Use the Python-based implementation nx.generators.directed._random_k_out_graph_python(1000, 5, alpha=1) References ---------- .. [1] Peterson, Nicholas R., and Boris Pittel. "Distance between two random `k`-out digraphs, with and without preferential attachment." arXiv preprint arXiv:1311.5961 (2013) . rzalpha must be positive)rT_random_k_out_graph_numpy ImportError_random_k_out_graph_python)r(rrr^rsr s rr r sMp qy122I(u$GG I)!4HHIs ::c SSKn[R"U[RS9nUR U5nUR US5nUR X5n X-n UR U5n [X-5Hn URXx5n U(aURXyU - S9nO XnSX'URXyX- - S9nXU 'URX5 X==S- ss'U S- n X==S- ss'XU:XdMSX'M U$)Nrr)T)r5rF) numpyr!rrSarangefullzerosr&r<r%)r(rrr^rsr npr*rZremaining_maskweights total_weight out_strengthsrorxriu_weights rrrs qr7A IIaLEWWQ%NggaG9LHHQKM 15\ KK- .  E|%; rs 3 T2? 3? DT21 31 hT2# 3# LT2    R 3R jT2L 3L ^T2\I3\I~  <  r