Algebraic Connectivity of Interdependent Networks

Journal article (2014)
Department
Network Architectures & Services (NAS) (EEMCS) (TU Delft)
Copyright: © publisher and authors
DOI: https://doi.org/doi:10.1016/j.physa.2014.02.043
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Published Date

14-06-2014

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Source:

Physica A: Statistical Mechanics and its Applications, volume 404, 2014, Pre-print version

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Network Architectures & Services (NAS)

Abstract

The algebraic connectivity UN-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 suffcient 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.