Spectrum of Complex Networks
Spectrum of Complex Networks
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DOI：
10.24166/im.03.2019
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Daniel Montealegre;V. Vu
中科院分区：
文献类型：
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作者：
Daniel Montealegre;V. Vu
复杂网络的研究是近几十年来科学界最活跃的领域之一。网络（或表示它们的图）的谱特性具有根本的重要性。研究人员已经研究这些性质多年，并根据数值数据，提出了一些问题的分布特征值和特征向量。在本文中，我们给出了其中一些问题的解决方案。特别是，我们确定的限制分布的（大部分）的频谱的网络的大小增长到无穷大，并表明，领导的本征向量强烈本地化。我们关注的优先连接图，这是最流行的数学模型增长的复杂网络。另一方面，我们的分析是一般性的，可以应用于其他模型。
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these properties for many years, and, based on numerical data, have raised a number of questions about the distribution of the eigenvalues and eigenvectors. In this paper, we give the solution to some of these questions. In particular, we determine the limiting distribution of (the bulk of) the spectrum as the size of the network grows to infinity and show that the leading eigenvectors are strongly localized. We focus on the preferential attachment graph, which is the most popular mathematical model for growing complex networks. Our analysis is, on the other hand, general and can be applied to other models.