wgP="dZddlZddlmZddlZddlmZddlm Z m Z m Z gdZ e dejdd dd Ze dejdd dd Ze d ejdd dd Ze dejdd  ddZe dejdd ddZe dejdd ddZy)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_graphctd|tj}|jstjd|d}|dk(r|S|j ddddg}t d|D]X}|Dcgc] }|| }}td||d} |j || |jd|| xxdz cc<Z|Scc}w)aBReturns 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 Graphc|SN)xs a/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/generators/directed.pykernelzgn_graph..kernelGsHr) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingrGdssourceddisttargets rrrsT A|RZZ8A ==?LMM ~  AvJJq! QB1+#%&aq &&"14dCAF 66" !  6 a  H 's7C cdtd|tj}|jstjd|dk(r|St d|D]X}|j d|}|j|kr|dk7rt|j|}|j||Z|S)aReturns 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) rrr r!r"r$ randrangerandomnext successorsr#)r&pr'rr(r*r-s rr r [sN A|RZZ8A ==?LMMAv1+#6* ;;=1 1!,,v./F 66" # HrrcPtd|tj}|jstjd|dk(r|St d|D]N}|j d|}|j|D]}|j|||j||P|S)a$Returns the growing network with copying (GNC) digraph with `n` nodes. The GNC graph is built by adding nodes one at a time with a link to one previously added node (chosen uniformly at random) and to all of that node's successors. Parameters ---------- n : int The number of nodes for the generated graph. create_using : NetworkX graph constructor, optional (default DiGraph) Graph type to create. If graph instance, then cleared before populated. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. References ---------- .. [1] P. L. Krapivsky and S. Redner, Network Growth by Copying, Phys. Rev. E, 71, 036118, 2005k.}, rrrr) rrr r!r"r$r/r2r#)r&r'rr(r*r-succs rr r s2 A|RZZ8A ==?LMMAv1+#6*LL( %D JJvt $ % 66" # Hrcfd}|>t|dr2t|tjstjd|} ntjgd} |dkr t d|dkr t d|dkr t dt ||z|zd z d k\r t d |dkr t d |dkr t d td| jDg} td| jDg} t| j} | Dcgc]}t|tjs|!} }t| dkDrtd| Ddz}nd}t| krj!}||kr#|}|dz }| j#||| | |}n?|||zkr|| | |}|| | |}n"|| | |}|}|dz }| j#|| j%||| j#|| j#|t| |kr| Scc}w)ucReturns a scale-free directed graph. Parameters ---------- n : integer Number of nodes in graph alpha : float Probability for adding a new node connected to an existing node chosen randomly according to the in-degree distribution. beta : float Probability for adding an edge between two existing nodes. One existing node is chosen randomly according the in-degree distribution and the other chosen randomly according to the out-degree distribution. gamma : float Probability for adding a new node connected to an existing node chosen randomly according to the out-degree distribution. delta_in : float Bias for choosing nodes from in-degree distribution. delta_out : float Bias for choosing nodes from out-degree distribution. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. 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|dkDrCt||z}||t|zz }j|krj|Sj|S)Nr)lenr0choice) candidates node_listdeltabias_sump_deltars r _choose_nodez&scale_free_graph.._choose_nodesW 199~-H(S_"<=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.c3.K|] \}}||gzywrr.0idxcounts r z#scale_free_graph..s = Uesem =c3.K|] \}}||gzywrrrCs rrGz#scale_free_graph..s < Uesem ."s8QS[8s!r)hasattr isinstancer MultiDiGraphr" ValueErrorabssum out_degree in_degreelistnodesnumbersNumberr9maxr0r%r#)r&alphabetagammadelta_in delta_outr initial_graphr@r(vswsr< numeric_nodescursorrvws ` rr r sJ|' W]F%C-9""#JK K  OO4 5 z-.. qy,-- z-.. 54<% # %&$.9::!|1221}233 =alln =r BB >-JQKMK =A8-881< a&1* KKM u9A aKF   Q RH5A  RI6ARH5A RI6AA aKF   Q  1a !  ! I a&1*L H]Ls /IIc |rtj}fd}ntj}fd}tj||}t |}|D]# |j fd| |D%|S)a_Returns a random `k`-out graph with uniform attachment. A random `k`-out graph with uniform attachment is a multidigraph generated by the following algorithm. For each node *u*, choose `k` nodes *v* uniformly at random (with replacement). Add a directed edge joining *u* to *v*. Parameters ---------- n : int The number of nodes in the returned graph. k : int The out-degree of each node in the returned graph. self_loops : bool If True, self-loops are allowed when generating the graph. with_replacement : bool If True, neighbors are chosen with replacement and the returned graph will be a directed multigraph. Otherwise, neighbors are chosen without replacement and the returned graph will be a directed graph. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- NetworkX graph A `k`-out-regular directed graph generated according to the above algorithm. It will be a multigraph if and only if `with_replacement` is True. Raises ------ ValueError If `with_replacement` is False and `k` is greater than `n`. See also -------- random_k_out_graph Notes ----- The return digraph or multidigraph may not be strongly connected, or even weakly connected. If `with_replacement` is True, this function is similar to :func:`random_k_out_graph`, if that function had parameter `alpha` set to positive infinity. c@s|hz fdtDS)Nc3RK|]}jt ywr)r:rU)rDirVrs rrGz=random_uniform_k_out_graph..sample..s?DKKU ,?s$')r$rerVkr self_loopss `rsamplez*random_uniform_k_out_graph..samples  ?eAh? ?rcJs||hz }jt|Sr)rorUrls rroz*random_uniform_k_out_graph..samples& ;;tE{A. .rc3&K|]}|f ywrr)rDreus rrGz-random_uniform_k_out_graph..s:A!Q:s)rrOr rsetadd_edges_from) r&rmrnwith_replacementrr'ror(rVrrs `` ` @rrandom_uniform_k_out_graphrvPswt(  @ zz|  / q,'A FE ; :5)9::; Hrc |dkr tdtj|tj}t |Dcic]}||c}}t ||zD]}|j |jD cgc] \}} | |ks |c} }} |st | || i} n t } t|| z |}|j| |||xxdz cc<|Scc}wcc} }w)aKReturns 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) rPrrrOrr$r:rSrr#) r&rmrZrnrr(reweightsrkr+rr adjustments rr r sJ qy122 qr7A+Aq%x+,G 1q5\  KKq||~?tq!Q? @ !WQZ1J J Gj0t < 1a a   H,?s C)? C. C. )NNN)NN)g= ףp=?gHzG?g?g?rNN)TTN)TN)__doc__rW collectionsrnetworkxrnetworkx.generators.classicrnetworkx.utilsrrr__all__ _dispatchablerr r r rvr rrrrsg 3NN T2? 3? DT21 31 hT2# 3# LT2    R 3R jT2L 3L ^T2R 3R r