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A new measure of network efficiency

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  • Hollingshad, Nicholas W.
  • Turalska, Malgorzata
  • Allegrini, Paolo
  • West, Bruce J.
  • Grigolini, Paolo

Abstract

We address the issue of the dynamical origin of scale-free link distributions. We study a two-dimensional lattice of cooperatively interacting units. Although the units interact only with the four nearest neighbors, a sufficiently large cooperation strength generates dynamically a scale-free network with the power law index ν approaching 1. We explain this result by using a new definition of network efficiency determined by the Euclidean distance between correlated units. According to this definition the link distribution favoring long-range connections makes efficiency increase. We embed an ad hoc scale-free network with power index ν≥1 into a Euclidean two-dimensional space and show that the network efficiency becomes maximal as ν approaches 1. We therefore conclude that ν=1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency.

Suggested Citation

  • Hollingshad, Nicholas W. & Turalska, Malgorzata & Allegrini, Paolo & West, Bruce J. & Grigolini, Paolo, 2012. "A new measure of network efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1894-1899.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1894-1899
    DOI: 10.1016/j.physa.2011.11.017
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    References listed on IDEAS

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    1. Barabási, Albert-László & Ravasz, Erzsébet & Vicsek, Tamás, 2001. "Deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(3), pages 559-564.
    2. Bianco, Simone & Geneston, Elvis & Grigolini, Paolo & Ignaccolo, Massimiliano, 2008. "Renewal aging as emerging property of phase synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1387-1392.
    3. Gu, Yuying & Sun, Jitao, 2010. "A tree-like complex network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 171-178.
    4. Chen, Mu & Yu, Boming & Xu, Peng & Chen, Jun, 2007. "A new deterministic complex network model with hierarchical structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 707-717.
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    Cited by:

    1. Mahmoodi, Korosh & West, Bruce J. & Grigolini, Paolo, 2020. "On the dynamical foundation of multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Allegrini, Paolo & Paradisi, Paolo & Menicucci, Danilo & Laurino, Marco & Bedini, Remo & Piarulli, Andrea & Gemignani, Angelo, 2013. "Sleep unconsciousness and breakdown of serial critical intermittency: New vistas on the global workspace," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 32-43.
    3. Paradisi, Paolo & Allegrini, Paolo, 2015. "Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 451-462.

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