ó žÃÒYc @ sºdZddlmZddlZyddlmZd„ZWnek r[d„ZnXddlZ dgZ d„Z d „Z d „Z d „Zdddddd d dd„ZdS(s9Functions for generating graphs with community structure.iÿÿÿÿ(tdivisionN(tzetacC s t||ƒS(N(t_zeta(txtqt tolerance((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyRscC s`d}tdƒ }d}x@t||ƒ|kr[|}|d|||7}|d7}qW|S(sThe Hurwitz zeta function, or the Riemann zeta function of two arguments. ``x`` must be greater than one and ``q`` must be positive. This function repeatedly computes subsequent partial sums until convergence, as decided by ``tolerance``. itinfi(tfloattabs(RRRtztz_prevtk((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyRs  tLFR_benchmark_graphcC sAtjj||ƒ}x%||kr<tjj||ƒ}qW|S(sôReturns a random value chosen from the Zipf distribution, guaranteed to be less than or equal to the value ``threshold``. Repeatedly draws values from the Zipf distribution until the threshold is met, then returns that value. (tnxtutilstzipf_rv(tgammatxmint thresholdtresult((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyt_zipf_rv_below1scC slxVt|ƒD]H}g}x)||ƒsD|jt|||ƒƒqW||ƒr |Sq Wtjdƒ‚dS(s6Returns a list of numbers obeying a power law distribution, with some additional restrictions. ``gamma`` and ``low`` are the parameters for the Zipf distribution. ``high`` is the maximum allowed value for values draw from the Zipf distribution. For more information, see :func:`_zipf_rv_below`. ``condition`` and ``length`` are Boolean-valued functions on lists. While generating the list, random values are drawn and appended to the list until ``length`` is satisfied by the created list. Once ``condition`` is satisfied, the sequence generated in this way is returned. ``max_iters`` indicates the number of times to generate a list satisfying ``length``. If the number of iterations exceeds this value, :exc:`~networkx.exception.ExceededMaxIterations` is raised. s#Could not create power law sequenceN(trangetappendRR tExceededMaxIterations(Rtlowthight conditiontlengtht max_iterstitseq((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyt_powerlaw_sequence?s c C s|}d}||d|}d}d} xÎt| |ƒ|krú||kratjdƒ‚nd} xDtt|ƒ|dƒD])} | | | dt|||ƒ7} qW| |krÕ|}||d|}n|}||d|}|d7}q-Wt|ƒS(s7Returns a minimum degree from the given average degree.iiisCould not match average_degree(RR RRtintRtround( Rtaverage_degreet max_degreeRRt min_deg_topt min_deg_bott min_deg_midtitrst mid_avg_degR((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyt_generate_min_degree]s&   c C sg|D]}tƒ^q}t|ƒ}tt|ƒƒ}xÂt|ƒD]´}|jƒ} tjtt|ƒƒƒ} t|| d|ƒ} | || kr°|| j| ƒn |j | ƒt|| ƒ|| krñ|j || jƒƒn|sG|SqGWd} t j | ƒ‚dS(sPReturns a list of sets, each of which represents a community in the graph. ``degree_sequence`` is the degree sequence that must be met by the graph. ``community_sizes`` is the community size distribution that must be met by the generated list of sets. ``mu`` is a float in the interval [0, 1] indicating the fraction of intra-community edges incident to each node. ``max_iters`` is the number of times to try to add a node to a community. This must be greater than the length of ``degree_sequence``, otherwise this function will always fail. If the number of iterations exceeds this value, :exc:`~networkx.exception.ExceededMaxIterations` is raised. The communities returned by this are sets of integers in the set {0, ..., *n* - 1}, where *n* is the length of ``degree_sequence``. is:Could not assign communities; try increasing min_communityN( tsettlentlistRtpoptrandomtchoiceR!taddRR R( tdegree_sequencetcommunity_sizestmuRt_RtntfreeRtvtctstmsg((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyt_generate_communitiesws    gH¯¼šò×z>iôc  sô| dk rtj| ƒn|dks:tjdƒ‚n|dksXtjdƒ‚nd|koodkns†tjdƒ‚n|dkr›ˆ}n.d|ko²ˆknsÉtjdƒ‚n|dk|dkAsñtjdƒ‚n|dkrt|||| | ƒ}n||} } d„}‡fd †}t|| | ||| ƒ}|dkrst|ƒ}n|dkrŽt|ƒ}n||} } ‡fd †}‡fd †}t|| | ||| ƒ}| d ˆ9} t |||| ƒ}tj ƒ}|j t ˆƒƒx×|D]Ï}xÆ|D]¾}xP|j |ƒt||d|ƒkr‚tjt|ƒƒ}|j||ƒq3WxQ|j |ƒ||krÖtjt ˆƒƒ}||kr†|j||ƒq†q†W||j|d >> from networkx.algorithms.community import LFR_benchmark_graph >>> n = 250 >>> tau1 = 3 >>> tau2 = 1.5 >>> mu = 0.1 >>> G = LFR_benchmark_graph(n, tau1, tau2, mu, average_degree=5, ... min_community=20, seed=10) Continuing the example above, you can get the communities from the node attributes of the graph:: >>> communities = {frozenset(G.nodes[v]['community']) for v in G} Notes ----- This algorithm differs slightly from the original way it was presented in [1]. 1) Rather than connecting the graph via a configuration model then rewiring to match the intra-community and inter-community degrees, we do this wiring explicitly at the end, which should be equivalent. 2) The code posted on the author's website [2] calculates the random power law distributed variables and their average using continuous approximations, whereas we use the discrete distributions here as both degree and community size are discrete. Though the authors describe the algorithm as quite robust, testing during development indicates that a somewhat narrower parameter set is likely to successfully produce a graph. Some suggestions have been provided in the event of exceptions. References ---------- .. [1] "Benchmark graphs for testing community detection algorithms", Andrea Lancichinetti, Santo Fortunato, and Filippo Radicchi, Phys. Rev. E 78, 046110 2008 .. [2] http://santo.fortunato.googlepages.com/inthepress2 istau1 must be greater than onestau2 must be greater than oneis!mu must be in the interval [0, 1]s)max_degree must be in the interval (0, n]s8Must assign exactly one of min_degree and average_degreecS st|ƒddkS(Nii(tsum(R((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pytjsc st|ƒˆkS(N(R+(R(R5(sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyR=ksc st|ƒˆkS(N(R<(R(R5(sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyR=}sc st|ƒˆkS(N(R<(R(R5(sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyR=~si t communityN(tNoneR.tseedR t NetworkXErrorR)RtmintmaxR;tGraphtadd_nodes_fromRtdegreeR!R/R,tadd_edgetnodes(R5ttau1ttau2R3R"t min_degreeR#t min_communityt max_communityttolRR@RRRRtdeg_seqtcommst communitiestGR8tuR7((R5sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyR §sX¬               * (t__doc__t __future__RR.t scipy.specialRRt ImportErrortnetworkxR t__all__RRR)R;R?R (((sˆ/private/var/folders/w6/vb91730s7bb1k90y_rnhql1dhvdd44/T/pip-build-w4MwvS/networkx/networkx/algorithms/community/community_generators.pyt s"          0