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摘要翻译：
研究了任意度分布的随机图中巨连通分量的性质。我们集中讨论度-度相关性。证明了巨连通分量中相邻节点的相关性，并导出了联合最近邻度概率分布的解析公式。利用这些结果，我们描述了极大熵连通随机图中的相关。我们证明连通图是不协调的，关联与一次结点（叶）的存在密切相关。我们提出了一个生成连通随机图的高效算法。我们用几个例子来说明我们的结果。
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英文标题：
《Correlations in connected random graphs》
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作者：
Piotr Bialas, Andrzej K. Ole\'s
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最新提交年份：
2010
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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：Other Condensed Matter 其他凝聚态物质
分类描述：Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
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英文摘要：
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe the correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.
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PDF链接：
https://arxiv.org/pdf/710.3319
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