Algebraic connectivity of interdependent networks

作者：Martin Hernandez J^*; Wang H; Van Mieghem P; D'Agostino G

来源：Physica A: Statistical Mechanics and Its Applications , 2014, 404: 92-105.

DOI：10.1016/j.physa.2014.02.043

• Network of networks
• Synchronization
• Laplacian
• Spectral properties
• System of systems

The algebraic connectivity mu(N-1), i.e. the second smallest eigenvalue of the Laplacian matrix, plays a crucial role in dynamic phenomena such as diffusion processes, synchronization stability, and network robustness. In this work we study the algebraic connectivity in the general context of interdependent networks, or network-of-networks (NoN). The present work shows, both analytically and numerically, how the algebraic connectivity of NoNs experiences a transition. The transition is characterized by a saturation of the algebraic connectivity upon the addition of sufficient coupling links (between the two individual networks of a NoN). In practical terms, this shows that NoN topologies require only a fraction of coupling links in order to achieve optimal diffusivity. Furthermore, we observe a footprint of the transition on the properties of Fiedler's spectral bisection.

• 出版日期2014-6-15