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Complexity vs. stability in small-world networks

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  • Sinha, Sitabhra

Abstract

According to the May–Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against this observation is that it is valid only for random networks, and therefore does not apply to real-world networks, which presumably are structured. Here, we examine how the introduction of small-world topological structure into networks affects their stability. Our results indicate that, in structured networks, the parameter values at which the stability–instability transition occurs with increasing complexity is identical to that predicted by the May–Wigner criteria. However, the nature of the transition, as measured by the finite-size scaling exponent, appears to change as the network topology transforms from regular to random, with the small-world regime as the cross-over region. This behavior is related to the localization of the largest eigenvalues along the real axis in the eigenvalue plain with increasing regularity in the network.

Suggested Citation

  • Sinha, Sitabhra, 2005. "Complexity vs. stability in small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 147-153.
  • Handle: RePEc:eee:phsmap:v:346:y:2005:i:1:p:147-153
    DOI: 10.1016/j.physa.2004.08.062
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    Cited by:

    1. Kim, Jongkwang & Wilhelm, Thomas, 2008. "What is a complex graph?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2637-2652.
    2. Hisi, Andreia N.S. & Guimarães, Paulo R. & de Aguiar, Marcus A.M., 2010. "The role of predator overlap in the robustness and extinction of a four species predator–prey network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4725-4733.
    3. Heiberger, Raphael H., 2014. "Stock network stability in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 376-381.
    4. Fathin Faizah Said, 2017. "Global Banking on the Financial Network Modelling: Sectorial Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 227-253, February.
    5. Sheri M. Markose, 2012. "Systemic Risk from Global Financial Derivatives; A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax," IMF Working Papers 12/282, International Monetary Fund.
    6. Markose, Sheri & Giansante, Simone & Shaghaghi, Ali Rais, 2012. "‘Too interconnected to fail’ financial network of US CDS market: Topological fragility and systemic risk," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 627-646.

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