ó ú£Õ\c@sdZddlmZdjdddgƒZddd d gZdd lmZdd lm Z dd l m Z ddl Z ddl Z ddlZddlZddd„Zddddd„Zdd„Zddddd„Zdddddd„ZdS(s" Generators for geometric graphs. iÿÿÿÿ(tprint_functions sAric Hagberg (hagberg@lanl.gov)s Dan Schult (dschult@colgate.edu)s!Ben Edwards (BJEdwards@gmail.com)trandom_geometric_grapht waxman_graphtgeographical_threshold_graphtnavigable_small_world_graph(t bisect_left(treduce(tproductNicCs0tjƒ}d|_|jt|ƒƒ|dkr{xW|D]9}gtd|ƒD]}tjƒ^qQ|j|d>> G = nx.random_geometric_graph(20,0.1) Notes ----- This uses an `n^2` algorithm to build the graph. A faster algorithm is possible using k-d trees. The pos keyword can be used to specify node positions so you can create an arbitrary distribution and domain for positions. If you need a distance function other than Euclidean you'll have to hack the algorithm. E.g to use a 2d Gaussian distribution of node positions with mean (0,0) and std. dev. 2 >>> import random >>> n=20 >>> p=dict((i,(random.gauss(0,2),random.gauss(0,2))) for i in range(n)) >>> G = nx.random_geometric_graph(n,0.2,pos=p) References ---------- .. [1] Penrose, Mathew, Random Geometric Graphs, Oxford Studies in Probability, 5, 2003. sRandom Geometric Graphitpostdatacss#|]\}}||dVqdS(iN((t.0tatb((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pys csiN(tnxtGraphtnametadd_nodes_fromtrangetNonetrandomtnodetset_node_attributestnodestTruetpoptsumtziptadd_edge(tntradiustdimRtGtiRtutdutputvtdvtpvtd((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pyR!s"1    :   c Cstjƒ}|jgt|ƒD] }|^qƒ|dkrlx>|D] }tjdƒ|j|d>> G = nx.geographical_threshold_graph(20,50) Notes ----- If weights are not specified they are assigned to nodes by drawing randomly from an the exponential distribution with rate parameter `\lambda=1`. To specify a weights from a different distribution assign them to a dictionary and pass it as the weight= keyword >>> import random >>> n = 20 >>> w=dict((i,random.expovariate(5.0)) for i in range(n)) >>> G = nx.geographical_threshold_graph(20,50,weight=w) If node positions are not specified they are randomly assigned from the uniform distribution. References ---------- .. [1] Masuda, N., Miwa, H., Konno, N.: Geographical threshold graphs with small-world and scale-free properties. Physical Review E 71, 036108 (2005) .. [2] Milan Bradonjić, Aric Hagberg and Allon G. Percus, Giant component and connectivity in geographical threshold graphs, in Algorithms and Models for the Web-Graph (WAW 2007), Antony Bonato and Fan Chung (Eds), pp. 209--216, 2007 gð?tweightiRN( R RRRRRt expovariateRRtadd_edges_fromtgeographical_threshold_edges( RtthetatalphaRRR(RR$R ((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pyRhs? &  !  :c csÂ|jdtƒ}x©|r½|jƒ\}}|d}|d}xv|D]n\}} | d} | d} tjtd„t|| ƒDƒƒƒ} || || |krH||fVqHqHWqWdS(NR R(Rcss#|]\}}||dVqdS(iN((R R R ((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pys Äs(RRRtmathtsqrtRR( RR,R-RR!R"twuR#R$R%twvR&tr((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pyR+¹s     (gš™™™™™Ù?gš™™™™™¹?iicCsttjƒ}|jt|ƒƒ|\}}}} xI|D]A}|||tjƒ|| |tjƒf|j|d= 1isq must be >= 0sr must be >= 1trepeatcss%|]\}}t||ƒVqdS(N(tabs(R R R ((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pys WsiÿÿÿÿN(R tNetworkXExceptionRRtseedtDiGraphR3RRRRRtappendtutilstcumulative_sumRtuniform(RtptqR2RRGRRtp1tprobstp2R'tcdft_ttarget((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pyR s0(          #(iiii(t__doc__t __future__Rtjoint __author__t__all__tbisectRt functoolsRt itertoolsRR.RtsystnetworkxR RRRR+RR(((sU/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/generators/geometric.pyts&   $ GP X