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摘要翻译：
复杂网络表现出各种类型的渗流转变。我们指出，单凭度分布和度-度相关不足以描述不同的渗流临界现象。这表明，真正的结构相关性是表征网络的一个重要因素。作为相关性的一个特征，我们研究了在$m_n(h)$中的缩放行为，即大小为$h$的有限环的数目，相对于网络大小$n$。我们发现度分布不太宽的网络可分为两类，分别为$M_n(h)\sim（{常数}）$和$M_n(h)\sim(\lnn)^\psi$。这种分类与根据渗流临界现象进行的分类是一致的。
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英文标题：
《Percolation and Loop Statistics in Complex Networks》
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作者：
Jae Dong Noh (UOS)
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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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英文摘要：
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a genuine structural correlation is an essential ingredient in characterizing networks. As a signature of the correlation we investigate a scaling behavior in $M_N(h)$, the number of finite loops of size $h$, with respect to a network size $N$. We find that networks, whose degree distributions are not too broad, fall into two classes exhibiting $M_N(h)\sim ({constant})$ and $M_N(h) \sim (\ln N)^\psi$, respectively. This classification coincides with the one according to the percolation critical phenomena.
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PDF链接：
https://arxiv.org/pdf/707.056
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