+ )iRt^RIt^RIHt.R Ot]!^4R Rl4tRt]!^4R Rl4tRt ]!^4R Rl4t ]!^4RRl4t ]!^4RR l4t R#)zS Utilities for generating random numbers, random sequences, and random selections. N)py_random_statecl\V4Uu.uFq2PV^, 4NK up#uupi)zC Return sample sequence of length n from a power law distribution. )range paretovariate)nexponentseedis&&& \/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/utils/random_sequence.pypowerlaw_sequencer s- 70is_valid_tree_degree_sequence..<s0CqFCsT)Fz1tree must have one more node than number of edges)Fz8nontrivial tree must have strictly positive node degrees)T)listlensumany)degree_sequenceseqnumber_of_nodestwice_number_of_edgess& r is_valid_tree_degree_sequencer!sn*  C#hOH?22a7II 0C00C000PP OcV^8d \R4hV^8:d \R4hVR, p^V,pRVP4, pVP4p\WRV, ),,4pRRV, ,V,pWg,VR, ,VR, , W, 8:gKV#)aReturns a random value chosen from the Zipf distribution. The return value is an integer drawn from the probability distribution .. math:: p(x)=\frac{x^{-\alpha}}{\zeta(\alpha, x_{\min})}, where $\zeta(\alpha, x_{\min})$ is the Hurwitz zeta function. Parameters ---------- alpha : float Exponent value of the distribution xmin : int Minimum value seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- x : int Random value from Zipf distribution Raises ------ ValueError: If xmin < 1 or If alpha <= 1 Notes ----- The rejection algorithm generates random values for a the power-law distribution in uniformly bounded expected time dependent on parameters. See [1]_ for details on its operation. Examples -------- >>> nx.utils.zipf_rv(alpha=2, xmin=3, seed=42) 8 References ---------- .. [1] Luc Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986. zxmin < 1za <= 1.0g?) ValueErrorrandomint) alphaxminra1buvxts &&& r zipf_rvr+Asb ax$$ z$$ B 2A  $++-  KKM cBhK'' ( C!G_ # 5AG C (AE 1  HrcR.pRpVFpW#, pVPV4K VUu.uF q3V, NK up#uupi)zFReturns normalized cumulative distribution from discrete distribution.g)append) distributioncdf cumulativeelements& r cumulative_distributionr2sN %CJ  : 14 4Wj  44 4sAc^RIpVeTpM&Ve \V4pM\P!R4h\ V4Uu.uFqcP 4NK ppVUu.uFqP WX4^, NK p pV #uupiuupi)a  Return sample sequence of length n from a given discrete distribution or discrete cumulative distribution. One of the following must be specified. distribution = histogram of values, will be normalized cdistribution = normalized discrete cumulative distribution Nz8discrete_sequence: distribution or cdistribution missing)bisectr2nx NetworkXErrorrr! bisect_left) rr. cdistributionrr4r/r inputseqsrs &&&& r discrete_sequencer;s   !%l3 F  (-Qx0x! xH04< <8a  c % ) )8C < J 1 =s B BcV\V48d \R4h\4p\V4V8dVP\ W44K,\ V4#)zxReturns k items without replacement from a weighted sample. The input is a dictionary of items with weights as values. zsample larger than population)rr setaddweighted_choicer)mappingkrsamples&&& r random_weighted_samplerCsI  3w<899 UF f+/ ?712 <rcVP4\VP44,pVP4Fwr4W$,pV^8gKVu# R#)zmReturns a single element from a weighted sample. The input is a dictionary of items with weights as values. N)r!rvaluesitems)r@rrndrAws&& r r?r?sE ++-#gnn./ /C   7H r)r rr+r2r;rCr?)g@N)N)NNN)N) __doc__networkxr5networkx.utilsr__all__r rr+r2r;rCr?rrr rNs *  @@@= = @5>    r