ó ,µ[c @ sBdZddlmZddlmZddlZddlmZddl m Z ddl m Z ddl m Z d d d d d gZ e dƒdddd„ƒZe dƒddd„ƒZe dƒddd„ƒZe dƒdddddddd„ƒZe dƒeedd„ƒZe dƒedd„ƒZdS(sd Generators for some directed graphs, including growing network (GN) graphs and scale-free graphs. iÿÿÿÿ(tdivision(tCounterN(t empty_graph(tdiscrete_sequence(tweighted_choice(tpy_random_statetgn_grapht gnc_grapht gnr_graphtrandom_k_out_graphtscale_free_graphic C std|dtjƒ}|jƒs6tjdƒ‚n|d krNd„}n|dkr^|S|jddƒddg}xtd|ƒD]n}g|D]}||ƒ^q—}tdd|d|ƒd} |j|| ƒ|j dƒ|| cd7`. 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. itdefaults+create_using must indicate a Directed GraphcS s|S(N((tx((s;lib/python2.7/site-packages/networkx/generators/directed.pytkernelMsiit distributiontseedN( RtnxtDiGrapht is_directedt NetworkXErrortNonetadd_edgetrangeRtappend( tnR t create_usingRtGtdstsourcetdtdistttarget((s;lib/python2.7/site-packages/networkx/generators/directed.pyRs )      cC s¼td|dtjƒ}|jƒs6tjdƒ‚n|dkrF|Sxotd|ƒD]^}|jd|ƒ}|jƒ|kr¤|dkr¤t|j |ƒƒ}n|j ||ƒqVW|S(sìReturn 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 probabiliy `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. iR s+create_using must indicate a Directed Graphi( RRRRRRt randrangetrandomtnextt successorsR(RtpRRRRR((s;lib/python2.7/site-packages/networkx/generators/directed.pyR`s&  icC s°td|dtjƒ}|jƒs6tjdƒ‚n|dkrF|Sxctd|ƒD]R}|jd|ƒ}x'|j|ƒD]}|j||ƒq~W|j||ƒqVW|S(s#Return 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.}, iR s+create_using must indicate a Directed Graphi( RRRRRRR R#R(RRRRRRtsucc((s;lib/python2.7/site-packages/networkx/generators/directed.pyR•s  ig= ×£p=Ú?gHáz®Gá?gš™™™™™©?gš™™™™™É?ic s*‡fd†}|dks+t|dƒ r_tjd|dtjƒ} | jdddgƒn|} | jƒoz| jƒstjdƒ‚n|dkrªt d ƒ‚n|dkrÅt d ƒ‚n|dkràt d ƒ‚nt |||d ƒd kr t d ƒ‚n| j ƒ} x t | ƒ|kr%| |t | ƒ} | |t | ƒ} ˆj ƒ} | |kr˜t | ƒ}|| | jƒ|| ƒ}np| ||krá|| | jƒ|| ƒ}|| | jƒ|| ƒ}n'|| | jƒ|| ƒ}t | ƒ}| j||ƒ| d7} qW| S(sŒReturns 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 ndoes from in-degree distribution. delta_out : float Bias for choosing ndoes 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. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. 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 sOd}ˆjƒ}x6|D].\}}||||7}||krPqqW|S(Ng(R!(RRtdeltatpsumtcumsumtrRR(R(s;lib/python2.7/site-packages/networkx/generators/directed.pyt _choose_nodeîs  t_adjiR iiis%MultiDiGraph required in create_usingsalpha must be >= 0.sbeta must be >= 0.gð?g•Ö&è .>salpha+beta+gamma must equal 1.N(ii(ii(ii(RthasattrRRt MultiDiGraphtadd_edges_fromRt is_multigraphRt ValueErrortabstnumber_of_edgestlenR!t in_degreet out_degreeR(Rtalphatbetatgammatdelta_int delta_outRRR*RR2tpsum_intpsum_outR)tvtw((Rs;lib/python2.7/site-packages/networkx/generators/directed.pyR ¼s>2         ic  s¤|r*tjƒ}‡‡‡fd†}n!tjƒ}‡‡‡fd†}tj||ƒ}t|ƒ}x4|D],‰|j‡fd†|ˆ|ƒDƒƒqpW|S(s_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 s3ˆsˆ|h‰n‡‡fd†tˆƒDƒS(Nc3 s$|]}ˆjtˆƒƒVqdS(N(tchoicetlist(t.0ti(tnodesR(s;lib/python2.7/site-packages/networkx/generators/directed.pys hs(R(R=RC(tkRt self_loops(RCs;lib/python2.7/site-packages/networkx/generators/directed.pytsampleesc s&ˆs||h}nˆj|ˆƒS(N(RF(R=RC(RDRRE(s;lib/python2.7/site-packages/networkx/generators/directed.pyRFmsc3 s|]}ˆ|fVqdS(N((RAR=(tu(s;lib/python2.7/site-packages/networkx/generators/directed.pys us(RR-RRtsetR.( RRDREtwith_replacementRRRFRRC((RDRRERGs;lib/python2.7/site-packages/networkx/generators/directed.pytrandom_uniform_k_out_graph(s:    *c  sˆdkrtdƒ‚ntj|dtjƒ}t‡fd†|Dƒƒ}x±t||ƒD]Ÿ}|jg|jƒD]\}} | |kry|^qyƒ} |sÀti|| | 6ƒ} n tƒ} t|| d|ƒ}|j | |ƒ||cd7`. 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). isalpha must be positiveRc si|]}ˆ|“qS(((RAR=(R6(s;lib/python2.7/site-packages/networkx/generators/directed.pys Às Ri( R0RRR-RRR?R5RR( RRDR6RERRtweightsRBR=RRGt adjustment((R6s;lib/python2.7/site-packages/networkx/generators/directed.pyR ysD : (t__doc__t __future__Rt collectionsRtnetworkxRtnetworkx.generators.classicRtnetworkx.utilsRRRt__all__RRRRR tTrueRJR (((s;lib/python2.7/site-packages/networkx/generators/directed.pyts.    @ 4 &  j O