hP= SrSSKrSSKJr SSKrSSKJr SSKJ 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\ "S5\R"SSS 9SSj55rg)zd Generators for some directed graphs, including growing network (GN) graphs and scale-free graphs. N)Counter) empty_graph)discrete_sequencepy_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$N)xs N/var/www/html/env/lib/python3.13/site-packages/networkx/generators/directed.pykernelgn_graph..kernelGsHr) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingrGdssourceddisttargets rrrsT A|RZZ8A ==??LMM ~  AvJJq! QB1+#%&2aq 2&"14CAF 6" !  a  H 's<Ccr[SU[RS9nUR5(d[R"S5eUS:XaU$[ 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(rr)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%r0r3r$)r'r(rr)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)lenr1choice) candidates node_listdeltabias_sump_deltars 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 g7frrrEs rrIrJs >-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;rX)rFirYrs rrI=random_uniform_k_out_graph..sample..s!?hDKKU ,,hs'*)r%rhrYkr self_loopss `rsample*random_uniform_k_out_graph..samples  ?eAh? ?rcR>T(dX1- nTR[U5T5$r)rsrXrps rrsrts$ ;;tE{A. .rc3,># UH nTU4v M g7frr)rFrhus rrI-random_uniform_k_out_graph..s:)9A!Q)9s)r rRr!rsetadd_edges_from) r'rqrrwith_replacementrr(rsr)rYrws `` ` @rrandom_uniform_k_out_graphr|Psvt(  @ @ zz|  / q'A FE  :5)9:: Hrc US:a [S5e[R"U[RS9n[ UVs0sHofU_M sn5n[ X-5HnUR UR5VV s/sHupiX:dM UPM sn n5n U(d[ XU 05n O [ 5n [X{- US9nURX5 Xv==S- ss'M U$s snfs sn nf)a{Returns a random `k`-out graph with preferential attachment. A random `k`-out graph with preferential attachment is a multidigraph generated by the following algorithm. 1. Begin with an empty digraph, and initially set each node to have weight `alpha`. 2. Choose a node `u` with out-degree less than `k` uniformly at random. 3. Choose a node `v` from with probability proportional to its weight. 4. Add a directed edge from `u` to `v`, and increase the weight of `v` by one. 5. If each node has out-degree `k`, halt, otherwise repeat from step 2. For more information on this model of random graph, see [1]. Parameters ---------- n : int The number of nodes in the returned graph. k : int The out-degree of each node in the returned graph. alpha : float A positive :class:`float` representing the initial weight of each vertex. A higher number means that in step 3 above, nodes will be chosen more like a true uniformly random sample, and a lower number means that nodes are more likely to be chosen as their in-degree increases. If this parameter is not positive, a :exc:`ValueError` is raised. self_loops : bool If True, self-loops are allowed when generating the graph. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- :class:`~networkx.classes.MultiDiGraph` A `k`-out-regular multidigraph generated according to the above algorithm. Raises ------ ValueError If `alpha` is not positive. Notes ----- The returned multidigraph may not be strongly connected, or even weakly connected. References ---------- [1]: Peterson, Nicholas R., and Boris Pittel. "Distance between two random `k`-out digraphs, with and without preferential attachment." arXiv preprint arXiv:1311.5961 (2013). rzalpha must be positive)r()rr) rSr rrRrr%r;rVrr$) r'rqr]rrrr)rhweightsrnr,rw adjustments rr r sJ qy122 qr7A+A%x+,G 15\ KKq||~?~tq~? @ !QZ1J J G0t < 1 a  H,?s C,? C1 C1 )NNN)NN)g= ףp=?gHzG?g?g?rNN)TTN)TN)__doc__rZ collectionsrnetworkxr networkx.generators.classicrnetworkx.utilsrrr__all__ _dispatchablerr r r r|r rrrrs[ 3NN T2? 3? DT21 31 hT2# 3# LT2    R 3R jT2L 3L ^T2R 3R r