U 9v f%A @sdZddlZddlmZddlZddlmZddlm Z m Z m Z dddd d gZ e d dd dZ e d dd dZe ddddZe dddd Ze ddddZe dd dd ZdS)!zd Generators for some directed graphs, including growing network (GN) graphs and scale-free graphs. N)Counter) empty_graph)discrete_sequencepy_random_stateweighted_choicegn_graph gnc_graph gnr_graphrandom_k_out_graphscale_free_graphc std|tjd}|s"tddkr2dd|dkr>|S|ddddg}td|D]N}fd d |D}td||d d}||||d||d7<q\|S) aDReturns 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)xrr@/tmp/pip-unpacked-wheel-_lngutwb/networkx/generators/directed.pykernelFszgn_graph..kernelrcsg|] }|qSrr).0drrr Qszgn_graph..) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingrGZdssourcedisttargetrrrrs )    cCs|td|tjd}|s"td|dkr.|Std|D]>}|d|}||krj|dkrjt| |}| ||q8|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. r rrr) rrrrr r" randrangerandomnext successorsr!)r$pr%rr&r'r)rrrr Zs&  rcCsvtd|tjd}|s"td|dkr.|Std|D]8}|d|}||D]}|||qR|||q8|S)a$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.}, r rrr) rrrrr r"r*r-r!)r$r%rr&r'r)succrrrrs  = ףp=?HzG?皙?皙?c s2fdd} |dk r,ddl} | jdtdd|dk rTt|drT|dk rNtd |} n(|dk rlt|drl|} ntd d d g} | r| st d |dkrtd|dkrtd|dkrtdt |||ddkrtd|dkrtd|dkrtdt dd| Dg} t dd| Dg} t| }dd|D}t|dkrxtdd|Dd}nd}t| |kr.}||kr|}|d7}||| | ||}nJ|||kr| | ||}| | ||}n"| | ||}|}|d7}||| ||| || |q|| S)uReturns 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. create_using : NetworkX graph constructor, optional The default is a MultiDiGraph 3-cycle. If a graph instance, use it without clearing first. If a graph constructor, call it to construct an empty graph. .. deprecated:: 3.0 create_using is deprecated, use `initial_graph` instead. 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. csD|dkr:t||}||t|}|kr:|S|S)Nr)lenr+choice) candidates node_listdeltaZbias_sumZp_deltarrr _choose_nodes    z&scale_free_graph.._choose_nodeNrzThe create_using argument is deprecated and will be removed in the future. To create a scale free graph from an existing MultiDiGraph, use initial_graph instead.r) stacklevelZ_adjzFCannot set both create_using and initial_graph. Set create_using=None.)rr )r r)rrz&MultiDiGraph required in initial_graphzalpha 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.css|]\}}||gVqdSrrridxcountrrr 7sz#scale_free_graph..css|]\}}||gVqdSrrr=rrrr@8scSsg|]}t|tjr|qSr) isinstancenumbersNumberrr$rrrr>s z$scale_free_graph..css|]}t|jVqdSr)intrealrDrrrr@Asr )warningswarnDeprecationWarninghasattr ValueErrorr MultiDiGraphrZ is_multigraphr abssum out_degreeZ in_degreelistnodesr5maxr+r#r!)r$alphabetagammaZdelta_inZ delta_outr%rZ initial_graphr;rGr&vswsr8Z numeric_nodescursorrvwrr:rr spH           Tc sv|rt}fdd}nt}fdd}t||}t|}|D]"|fdd||DqN|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)r6rP)ri)rQrrrr@sz=random_uniform_k_out_graph..sample..)r"rZrQkr self_loops)rQrsamples z*random_uniform_k_out_graph..samplecss||h}t|Sr)rbrPr^r_rrrbs c3s|]}|fVqdSrrrrZ)urrr@sz-random_uniform_k_out_graph..)rrLrrsetZadd_edges_from) r$r`raZwith_replacementrr%rbr&rQr)r`rrardrrandom_uniform_k_out_graphos9  rfc sdkrtdtj|tjd}tfdd|D}t|D]h}|fdd|D}|sxt|||i} nt} t|| |d} | || || d 7<qB|S) 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%csi|] }|qSrrrc)rSrr sz&random_k_out_graph..csg|]\}}|kr|qSrr)rrZr)r`rrrsz&random_k_out_graph..r:r ) rKrrrLrr"r6rOrr!) r$r`rSrarr&weightsr]rdZ adjustmentrZr)rSr`rr sD )NNN)NN)NN)r1r2r3r4rNNN)TTN)TN)__doc__rB collectionsrZnetworkxrZnetworkx.generators.classicrZnetworkx.utilsrrr__all__rr rr rfr rrrrs@    B 4 & 9 O