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摘要翻译：
尽管大多数实际网络都包含有向和双向（互易）连接的混合，但互易性R$作为一个理论理解的主题很少受到关注。利用统计系综方法研究了具有任意度序列和一类广义度相关的网络的期望互易性。我们证明了度相关对于理解真实网络中的互易性是至关重要的，并揭示了相关对$R$贡献的层次结构。使用新的网络随机化方法的数值实验表明，与我们的解析估计非常吻合。
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英文标题：
《Reciprocity of Networks with Degree Correlations and Arbitrary Degree
Sequences》
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作者：
Gorka Zamora--L\'opez, Vinko Zlati\'c, Changsong Zhou, Hrvoje
\v{S}tefan\v{c}i\'c, J\"urgen Kurths
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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：
Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with an arbitrary degree sequence and a broad class of degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to $r$ is revealed. Numerical experiments using novel network randomization methods show very good agreement to our analytical estimations.
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PDF链接：
https://arxiv.org/pdf/706.3372
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