论文标题
复杂网络的特征值比率统计：疾病与随机性
Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness
论文作者
论文摘要
随机矩阵的连续特征值间距的比率分布已成为研究多体系统光谱特性的重要工具。本文数值研究了各种模型网络的特征值比率分布，即小世界，erdős-rényi随机，以及（dis）在相应的邻接矩阵中具有对角度障碍的分类随机。没有任何对角线障碍，这些模型网络的特征值比分布描绘了高斯正交集合（GOE）统计。添加对角线障碍后，根据疾病的强度，从GOE到泊松统计的逐渐过渡。采购泊松统计数据所需的关键障碍（WC）随着网络体系结构的随机性而增加。我们将WC与最大熵随机步行者所花费的时间联系起来，以达到稳态。这些分析将有助于了解特征值以外的其他网络动态（例如瞬态行为）的作用。
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios distribution of various model networks, namely, small-world, Erdős-Rényi random, and (dis)assortative random having a diagonal disorder in the corresponding adjacency matrices. Without any diagonal disorder, the eigenvalues ratio distribution of these model networks depict Gaussian orthogonal ensemble (GOE) statistics. Upon adding diagonal disorder, there exists a gradual transition from the GOE to Poisson statistics depending upon the strength of the disorder. The critical disorder (wc) required to procure the Poisson statistics increases with the randomness in the network architecture. We relate wc with the time taken by the maximum entropy random walker to reach the steady-state. These analyses will be helpful to understand the role of eigenvalues other than the principal one for various network dynamics such as transient behaviour.
