Gd%AZdZddlZddlmZddlZddlmZddlm Z m Z m Z gdZ e dddZ e ddd Ze d dd Ze d  ddZe dddZe dddZdS)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_graphctd|tj}|stjdd|dkr|S|ddddg}t d|D]c}fd|D}td|| d}||||d||xxdz cc<d|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 GraphNc|SN)xs .kernelFsHrc&g|] }|Srr).0drs r zgn_graph..Qs!&&&aq &&&r) distributionseed) rnxDiGraph is_directed NetworkXErroradd_edgerangerappend) nr create_usingr Gdssourcedisttargets ` rrrsR A|RZ888A ==??NLMMM ~    AvvJJq! QB1++&&&&2&&&"14dCCCAF 66""" !  6 a Hrctd|tj}|stjd|dkr|St d|D]n}|d|}||kr(|dkr"t| |}| ||o|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) rr!r"r#r$r& randrangerandomnext successorsr%)r(pr)r r*r,r.s rr r ZsL A|RZ888A ==??NLMMMAvv1++##6** ;;==1  1!,,v..//F 66"""" Hrrcxtd|tj}|stjd|dkr|St d|D]\}|d|}||D]}||||||]|S)a$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) rr!r"r#r$r&r0r3r%)r(r)r r*r,r.succs rr r s0 A|RZ888A ==??NLMMMAvv1++##6**LL(( % %D JJvt $ $ $ $ 66"""" Hr= ףp=?HzG?皙?皙?c fd} |!ddl} | dtd|$t|dr|t d|} n+|t|dr|} nt jgd } | r| st j d |dkrt d |dkrt d |dkrt d t||z|zdz dkrt d|dkrt d|dkrt dtd| Dg} td| Dg} t| }d|D}t!|dkrt#d|Ddz}nd}t!| |kr}||kr*|}|dz }||| | ||}nM|||zkr| | ||}| | ||}n)| | ||}|}|dz }||| ||| || |t!| |k| 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. c|dkrTt||z}||t|zz }|kr|S|S)Nr)lenr1choice) candidates node_listdeltabias_sump_deltar s r _choose_nodez&scale_free_graph.._choose_nodesh 1999~~-H(S__"<=G{{}}w&&{{9---{{:&&&rNrzThe 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) stacklevel_adjzFCannot set both create_using and initial_graph. Set create_using=None.))rr)rr)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.c3(K|] \}}||gzVdSrrridxcounts r z#scale_free_graph..7s, = = Uesem = = = = = =rc3(K|] \}}||gzVdSrrrIs rrLz#scale_free_graph..8s, < < Uesem < < < < < .>s)KKK1Z7>-J-JKQKKKrc3>K|]}t|jVdSr)intrealrRs rrLz#scale_free_graph..As*88QS[[888888rr)warningswarnDeprecationWarninghasattr ValueErrorr! MultiDiGraphr# is_multigraphr$abssum out_degree in_degreelistnodesr>maxr1r'r%)r(alphabetagammadelta_in delta_outr)r initial_graphrErVr*vswsrA numeric_nodescursorrvws ` rr r svP'''''  %     GL&$A$A  $X    $)G)G $AA 8 8 899A MMOOI 1 1IGHHH zz-... qyy,--- zz-... 54<% # %&&$..9:::!||12221}}2333 = =allnn = = =r B BB < `. 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. cNs|hz fdtDS)Nc3\K|]&}tV'dSr)r?ra)rirbr s rrLz=random_uniform_k_out_graph..sample..s5??DKKU ,,??????r)r&rorbkr self_loopss `rsamplez*random_uniform_k_out_graph..samples: $ ?????eAhh??? ?rcZs||hz }t|Sr)ryrarvs rryz*random_uniform_k_out_graph..samples0 $ ;;tE{{A.. .rc3 K|]}|fV dSrr)rrous rrLz-random_uniform_k_out_graph..s'::A!Q::::::r)r!r[r"rsetadd_edges_from) r(rwrxwith_replacementr r)ryr*rbr|s `` ` @rrandom_uniform_k_out_graphrosr/((  @ @ @ @ @ @ @ @ z||  / / / / / / / q,''A FFE ;; ::::5)9)9::::::: Hrcdkrtdtj|tj}t fd|D}t |zD]}|fd|D}|st |||i} nt } t|| z |} | || || xxdz cc<|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)ci|]}|Srr)rrords r z&random_k_out_graph..s+++Aq%+++rc&g|] \}}|k |Srr)rrorrws rrz&random_k_out_graph..s"???tq!Qr)r r) rZr!rr[rr&r?r_rr%) r(rwrdrxr r*weightsrur| adjustmentros `` rr r sH qyy1222 qr777A+++++++,,G 1q5\\   KK????q||~~??? @ @ # !WQZ11JJ J Gj0t < < < 1a a Hr)NNN)NN)r8r9r:r;rNNN)TTN)TN)__doc__rP collectionsrnetworkxr!networkx.generators.classicrnetworkx.utilsrrr__all__rr r r rr rrrrs 333333NNNNNNNNNN   ? ? ? ? D1 1 1 1 h# # # # L    u u u u pL L L L ^R R R R R R r