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Algebraic connectivity of interdependent networks

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

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.

Suggested Citation

  • Martín-Hernández, J. & Wang, H. & Van Mieghem, P. & D’Agostino, G., 2014. "Algebraic connectivity of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 92-105.
    • Handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:92-105
    DOI: 10.1016/j.physa.2014.02.043
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    References listed on IDEAS

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    1. Juan Chen & Jun-an Lu & Choujun Zhan & Guanrong Chen, 2012. "Laplacian Spectra and Synchronization Processes on Complex Networks," Springer Optimization and Its Applications, in: My T. Thai & Panos M. Pardalos (ed.), Handbook of Optimization in Complex Networks, edition 1, chapter 0, pages 81-113, Springer.
    2. Sergey V. Buldyrev & Roni Parshani & Gerald Paul & H. Eugene Stanley & Shlomo Havlin, 2010. "Catastrophic cascade of failures in interdependent networks," Nature, Nature, vol. 464(7291), pages 1025-1028, April.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    4. Lin, Peng & Jia, Yingmin, 2008. "Average consensus in networks of multi-agents with both switching topology and coupling time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 303-313.
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    Cited by:

    1. Li, Xin & Wu, Haotian & Scoglio, Caterina & Gruenbacher, Don, 2015. "Robust allocation of weighted dependency links in cyber–physical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 316-327.
    2. Rueda, Diego F. & Calle, Eusebi, 2017. "Using interdependency matrices to mitigate targeted attacks on interdependent networks: A case study involving a power grid and backbone telecommunications networks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 16(C), pages 3-12.
    3. Gafarov, F.M., 2016. "Emergence of the small-world architecture in neural networks by activity dependent growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 409-418.

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