摘要翻译:
给出了任意度分布的随机网络中元件尺寸完全分布的精确解。该解告诉我们,对于任意s,随机选择的节点属于大小为s的组件的概率。我们将我们的结果应用于具有三种最常研究的度分布--泊松、指数和幂律--的网络,以及网络上键渗流的团簇大小的计算,这些团簇大小对应于同一网络上SIR流行病过程的爆发大小。对于幂律度分布的特殊情况,我们证明了在巨分量形成的相变以下各处分量尺寸分布本身遵循幂律,而在巨分量存在时则呈指数形式。
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英文标题:
《Component sizes in networks with arbitrary degree distributions》
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作者:
M. E. J. Newman
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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一级分类:Physics 物理学
二级分类:Disordered Systems and Neural Networks 无序系统与神经网络
分类描述:Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜;随机、非周期和准周期系统的性质;无序介质中的传输;本地化;由缺陷和无序介导的现象;神经网络
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英文摘要:
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any s. We apply our results to networks with the three most commonly studied degree distributions -- Poisson, exponential, and power-law -- as well as to the calculation of cluster sizes for bond percolation on networks, which correspond to the sizes of outbreaks of SIR epidemic processes on the same networks. For the particular case of the power-law degree distribution, we show that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms, but takes an exponential form when a giant component is present.
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PDF链接:
https://arxiv.org/pdf/707.008