o hP=@sdZddlZddlmZddlZddlmZddlm Z m Z m Z gdZ e dej ddd dd d Ze dej ddd dd d Ze dej ddd dddZe dej ddd        dddZe dej ddd d ddZe dej ddd d!ddZdS)"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 std|tjd}|stddurdd|dkr|S|ddddg}td|D]'}fd d |D}td||d d}||||d||d7<q.|S) 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 GraphNcSs|SN)xrrp/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/networkx/generators/directed.pykernelGszgn_graph..kernelrcsg|]}|qSrr).0drrr Rszgn_graph..) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingrGdssourcedisttargetrrrrs *    rcCs|td|tjd}|std|dkr|Std|D]}|d|}||kr5|dkr5t| |}| ||q|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,rrrr [s'  r rcCsvtd|tjd}|std|dkr|Std|D]}|d|}||D]}|||q)|||q|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-r0r#)r&r'rr(r*r,succrrrrs  r= ףp=?HzG?皙?皙?csfdd}|durt|drt|tjstd|} ntgd} |dkr,td|dkr4td |dkr`. 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. csD|dkrt||}||t|}|kr|S|S)Nr)lenr.choice) candidates node_listdeltabias_sump_deltarrr _choose_nodes     z&scale_free_graph.._choose_nodeN_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.cs|] \}}||gVqdSrrridxcountrrr z#scale_free_graph..csrBrrrCrrrrFrGcSsg|] }t|tjr|qSr) isinstancenumbersNumberrr&rrrrz$scale_free_graph..css|]}t|jVqdSr)intrealrKrrrrF"sr)hasattrrHr MultiDiGraphr" ValueErrorabssum out_degree in_degreelistnodesr8maxr.r%r#)r&alphabetagammadelta_in delta_outr initial_graphr@r(vswsr; numeric_nodescursorrvwrr?rr sX >              &r c sv|rt}fdd}n t}fdd}t||}t|}|D]|fdd||Dq'|S)a_Returns a random `k`-out graph with uniform attachment. A random `k`-out graph with uniform attachment is a multidigraph generated by the following algorithm. For each node *u*, choose `k` nodes *v* uniformly at random (with replacement). Add a directed edge joining *u* to *v*. Parameters ---------- n : int The number of nodes in the returned graph. k : int The out-degree of each node in the returned graph. self_loops : bool If True, self-loops are allowed when generating the graph. with_replacement : bool If True, neighbors are chosen with replacement and the returned graph will be a directed multigraph. Otherwise, neighbors are chosen without replacement and the returned graph will be a directed graph. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- NetworkX graph A `k`-out-regular directed graph generated according to the above algorithm. It will be a multigraph if and only if `with_replacement` is True. Raises ------ ValueError If `with_replacement` is False and `k` is greater than `n`. See also -------- random_k_out_graph Notes ----- The return digraph or multidigraph may not be strongly connected, or even weakly connected. If `with_replacement` is True, this function is similar to :func:`random_k_out_graph`, if that function had parameter `alpha` set to positive infinity. cs&s|hfddtDS)Nc3s|] }tVqdSr)r9rV)ri)rWrrrrFrGz=random_uniform_k_out_graph..sample..)r$rdrWkr self_loops)rWrsamples z*random_uniform_k_out_graph..samplecss||h}t|Sr)rlrVrhrirrrls c3s|]}|fVqdSrrrrd)urrrFsz-random_uniform_k_out_graph..)rrPr rsetadd_edges_from) r&rjrkwith_replacementrr'rlr(rWr)rjrrkrnrrandom_uniform_k_out_graphPs:  rrc sdkrtdtj|tjd}tfdd|D}t|D]4}|fdd|D}|s`. 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'csi|]}|qSrrrm)rYrr sz&random_k_out_graph..csg|] \}}|kr|qSrr)rrdr)rjrrrrLz&random_k_out_graph..r?r) rQrrrPrr$r9rTrr#) r&rjrYrkrr(weightsrgrn adjustmentrdr)rYrjrr sE r )NNN)NN)r4r5r6r7rNN)TTN)TN)__doc__rI collectionsrnetworkxrnetworkx.generators.classicrnetworkx.utilsrrr__all__ _dispatchablerr rr rrr rrrrsB   B 4 &  O