摘要翻译：
通过引入不完全生长过程，提出了统一递归树(URT)的一个广义模型，该模型可能产生不连通的组件（簇）。该模型经历了一个有趣的相变，从单连通网络到由完全孤立节点组成的图。我们通过理论预测和数值模拟研究了度和组分尺寸的分布。对于非平凡情形，我们证明了网络具有指数次分布，而网络的元件尺寸分布服从幂律，这两者都与不完全生长过程有关。我们还预测了单个组分的生长动态。所有的解析解都成功地与计算机模拟进行了对比。
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英文标题：
《Degree and component size distributions in generalized uniform recursive
  tree》
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作者：
Zhongzhi Zhang, Shuigeng Zhou, Shanghong Zhao, Jihong Guan, and Tao
  Zou
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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：
  We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected network to a graph consisting of fully isolated nodes. We investigate the distributions of degree and component sizes by both theoretical predictions and numerical simulations. For the nontrivial cases, we show that the network has an exponential degree distribution while its component size distribution follows a power law, both of which are related to the imperfect growth process. We also predict the growth dynamics of the individual components. All analytical solutions are successfully contrasted with computer simulations.
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PDF链接：
https://arxiv.org/pdf/711.008