Algebraic connectivity of interdependent networks

J. Martín-Hernández, H. Wang, P. Van Mieghem, G. D'Agostino

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Abstract

The algebraic connectivity μN-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. © 2014 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)92 - 105
Number of pages14
JournalPhysica A: Statistical Mechanics and its Applications
Volume404
DOIs
Publication statusPublished - 15 Jun 2014

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

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