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arXiv physics/0702010physics.soc-ph
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链路空间与网络分析

Link-Space and Network Analysis

David M. D. Smith, Chiu Fan Lee, Neil F. Johnson, Jukka-Pekka Onnela

摘要:

许多网络都包含相关性,而传统的分析往往无法包含这一基本特征。在arXiv:0708.2176中,我们介绍了用于分析演化网络中度-度相关性的链接空间形式主义。在这个扩展版本中,我们提供了额外的数学细节和补充材料。我们探讨了一些常见的疏忽时,这些相关性不考虑在内,突出形式主义的重要性。该形式主义是基于一个统计描述的链接的分数l_{i,j}连接节点的度i和j。为了证明其使用,我们应用框架的一些教学网络模型,即随机附件,Barabasi-Albert优先附件和经典的鄂尔多斯和Renyi随机图。对于这三个模型,链接空间矩阵可以解析求解。我们应用的形式主义一个简单的单参数增长网络模型,其数值解的度度相关性的影响,所得到的度分布。我们还采用的形式主义,以获得两个非常简单的网络衰减模型,更具体地说,随机链接删除和随机节点删除的度分布。该形式主义允许详细分析网络内的相关性,我们还利用它来推导出任意度分布的完全非线性网络的形式。

英文摘要:

Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving networks. In this extended version, we provide additional mathematical details and supplementary material. We explore some of the common oversights when these correlations are not taken into account, highlighting the importance of the formalism. The formalism is based on a statistical description of the fraction of links l_{i,j} connecting nodes of degrees i and j. To demonstrate its use, we apply the framework to some pedagogical network models, namely, random-attachment, Barabasi-Albert preferential attachment and the classical Erdos and Renyi random graph. For these three models the link-space matrix can be solved analytically. We apply the formalism to a simple one-parameter growing network model whose numerical solution exemplifies the effect of degree-degree correlations for the resulting degree distribution. We also employ the formalism to derive the degree distributions of two very simple network decay models, more specifically, that of random link deletion and random node deletion. The formalism allows detailed analysis of the correlations within networks and we also employ it to derive the form of a perfectly non-assortative network for arbitrary degree distribution.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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