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arXiv 0711.2736physics.soc-phcond-mat.dis-nnphysics.comp-ph
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编织复杂网络

Knitted Complex Networks

Luciano da Fontoura Costa

摘要:

在相当大的程度上,复杂网络作为真实世界结构模型的持续重要性和流行性受到无标度分布以及各自隐含的枢纽的激励。与网络中边的顺序连接有关,路径代表复杂网络中另一种重要的双重连接模式(或基序)(例如,路径与诸如中间中心性的重要概念有关)。目前的工作提出了一个新的超类别的复杂网络的组织和/或构造的路径。提出了两种具体的网络类别,其特征在于:(i)PA网络,通过星路径变换Barabasi-Albert网络获得;和(ii)PN网络,通过执行涉及所有节点的渐进路径而不重复。这种新网络的重要性不仅在于其提供理论见解的潜力,而且还在于其作为现实世界结构的假定模型。这两个模型的连通性结构进行了研究相比,四个传统的复杂网络模型(埃尔多塞-雷尼,巴拉巴西-阿尔伯特,瓦特-Strogatz和地理模型)。描述了一系列有趣的结果,包括确证的两个模型的不同性质和考虑一套全面的测量和多变量统计方法的复杂网络的表征的重要性。

英文摘要:

To a considerable extent, the continuing importance and popularity of complex networks as models of real-world structures has been motivated by scale free degree distributions as well as the respectively implied hubs. Being related to sequential connections of edges in networks, paths represent another important, dual pattern of connectivity (or motif) in complex networks (e.g., paths are related to important concepts such as betweeness centrality). The present work proposes a new supercategory of complex networks which are organized and/or constructed in terms of paths. Two specific network classes are proposed and characterized: (i) PA networks, obtained by star-path transforming Barabasi-Albert networks; and (ii) PN networks, built by performing progressive paths involving all nodes without repetition. Such new networks are important not only from their potential to provide theoretical insights, but also as putative models of real-world structures. The connectivity structure of these two models is investigated comparatively to four traditional complex networks models (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz and a geographical model). A series of interesting results are described, including the corroboration of the distinct nature of the two proposed models and the importance of considering a comprehensive set of measurements and multivariated statistical methods for the characterization of complex networks.

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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