Year: 2017
Type: article
Abstract: 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 $\ensuremath{\beta}$ of the eigenfunctions of multilayer random networks follows a simple scaling law given by $\ensuremath{\beta}={x}^{*}/(1+{x}^{*})$, with ${x}^{*}=\ensuremath{\gamma}{({b}_{\mathrm{eff}}^{2}/L)}^{\ensuremath{\delta}}$, $\ensuremath{\delta}\ensuremath{\sim}1$, and ${b}_{\mathrm{eff}}$ being the effective bandwidth of the adjacency matrix of the network, whose size is $L$. The scaling law for $\ensuremath{\beta}$, 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.
Source: Physical review. E
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: European Commission, Fundação de Amparo à Pesquisa do Estado de São Paulo, Federación Española de Enfermedades Raras, Consejo Nacional de Ciencia y Tecnología, Ministerio de Economía y Competitividad, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Vicerrectoría de Investigación y Estudios de Posgrado, Benemérita Universidad Autónoma de Puebla, H2020 Future and Emerging Technologies
OpenAlex ID: W2554071340