Méndez-Bermúdez J A, de Arruda Guilherme Ferraz, Rodrigues Francisco A, Moreno Yamir
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil.
Phys Rev E. 2017 Jul;96(1-1):012307. doi: 10.1103/PhysRevE.96.012307. Epub 2017 Jul 7.
Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them. Here, we numerically demonstrate that the normalized localization length β of the eigenfunctions of multilayer random networks follows a simple scaling law given by β=x^{}/(1+x^{}), with x^{*}=γ(b_{eff}^{2}/L)^{δ}, δ∼1, and b_{eff} being the effective bandwidth of the adjacency matrix of the network, whose size is L. The scaling law for β, that we validate on real-world networks, might help to better understand criticality in multilayer networks and to predict the eigenfunction localization properties of them.
多层网络广泛存在于自然和人造系统中。这些网络的关键特性是它们的频谱和本征函数特征，因为它们决定了许多发生在其之上的动力学的临界特性。在这里，我们通过数值证明，多层随机网络本征函数的归一化局域长度β遵循一个简单的标度律，即β = x*/(1 + x*)，其中x* = γ(b_eff^2/L)^δ，δ ∼ 1，且b_eff是网络邻接矩阵的有效带宽，其大小为L。我们在真实世界网络上验证的β的标度律，可能有助于更好地理解多层网络中的临界性，并预测它们的本征函数局域特性。
