复杂网络的统计自相似性质
Statistical Self-Similar Properties of Complex Networks
摘要：
研究表明，许多复杂网络都具有独特的特征，这些特征在许多方面不同于随机网络和规则网络。虽然这些特征捕捉了复杂网络的重要特征，但它们的适用性取决于网络的类型。为了揭示复杂网络可能具有的普遍特征，本文采用聚类系数作为概率测度，从统计自相似性的角度对各种类型的复杂网络进行了系统的分析。我们发现，聚类系数的概率分布最能表征多重分形特征，而且该测度的支持度具有分维。这两个特征使我们能够以统一的方式描述复杂网络，同时也为理解复杂网络提供了不可预见的可能性。
英文摘要：
It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability depends on the type of networks. To unravel ubiquitous characteristics that complex networks may have in common, we adopt the clustering coefficient as the probability measure, and present a systematic analysis of various types of complex networks from the perspective of statistical self-similarity. We find that the probability distribution of the clustering coefficient is best characterized by the multifractal; moreover, the support of the measure had a fractal dimension. These two features enable us to describe complex networks in a unified way; at the same time, offer unforeseen possibilities to comprehend complex networks.
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