All Scale-Free Networks Are Sparse
All Scale-Free Networks Are Sparse
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DOI：
10.1103/physrevlett.107.178701
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发表时间：
2011-10-17
影响因子：
8.6
通讯作者：
Bassler, Kevin E.
中科院分区：
文献类型：
--
作者：
Del Genio, Charo I.;Gross, Thilo;Bassler, Kevin E.
我们研究了具有给定度序列的无标度网络的可实现性，表明可实现序列的分数在幂律指数的值0和2处经历了两次一阶转变。我们证实了这一发现的分析推理和数值方法，在这里提出的，基于极值参数，它可以适用于任何给定的度分布。我们的研究结果揭示了一个根本原因，为什么大型无标度网络没有限制的最小和最大程度必须稀疏。
We study the realizability of scale-free networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.