论文标题
Wigner的加权随机网络的半圆定律
The Wigner's Semicircle Law of Weighted Random Networks
论文作者
论文摘要
光谱图论提供了一种代数方法，可以使用代表网络结构的矩阵的特征值和特征向量研究加权网络的特征。但是，大型和复杂的网络（例如，社交网络）很难正确地表示其结构。如果特征值独立于大规模和复杂网络中的详细结构，那么我们可以避免难度。在本文中，我们阐明了Wigner的加权网络的半圆形定律，例如这种普遍性。该法律表明，当加权网络满足节点度的足够条件时，可以根据几个网络统计数据（平均程度，平均链路权重和平均平均链路权重）计算出归一化拉普拉斯矩阵的特征值（加权网络的特征值）。
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult for large-scale and complex networks (e.g., social network) to represent their structure as a matrix correctly. If there is a universality that the eigenvalues are independent of the detailed structure in large-scale and complex network, we can avoid the difficulty. In this paper, we clarify the Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix for weighted networks can be calculated from the a few network statistics (the average degree, the average link weight, and the square average link weight) when the weighted networks satisfy the sufficient condition of the node degrees and the link weights.
