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Universal fractal scaling of self-organized networks

Author

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  • Laurienti, Paul J.
  • Joyce, Karen E.
  • Telesford, Qawi K.
  • Burdette, Jonathan H.
  • Hayasaka, Satoru

Abstract

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.

Suggested Citation

  • Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:20:p:3608-3613
    DOI: 10.1016/j.physa.2011.05.011
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    References listed on IDEAS

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    1. Ramon Ferrer i Cancho & Christiaan Janssen & Ricard V. Solé, 2001. "The Topology of Technology Graphs: Small World Patterns in Electronic Circuits," Working Papers 01-05-029, Santa Fe Institute.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    3. H. Jeong & S. P. Mason & A.-L. Barabási & Z. N. Oltvai, 2001. "Lethality and centrality in protein networks," Nature, Nature, vol. 411(6833), pages 41-42, May.
    4. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    5. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    6. Martin J. Conyon & Mark R. Muldoon, 2006. "The Small World of Corporate Boards," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1321-1343.
    7. Marcus Kaiser & Claus C Hilgetag, 2006. "Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems," PLOS Computational Biology, Public Library of Science, vol. 2(7), pages 1-11, July.
    8. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    9. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    10. Martin J. Conyon & Mark R. Muldoon, 2006. "The Small World of Corporate Boards," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1321-1343, November.
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    Cited by:

    1. Blagus, Neli & Šubelj, Lovro & Bajec, Marko, 2012. "Self-similar scaling of density in complex real-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2794-2802.
    2. Hauke Ward & Leonie Wenz & Jan C. Steckel & Jan C. Minx, 2018. "Truncation Error Estimates in Process Life Cycle Assessment Using Input‐Output Analysis," Journal of Industrial Ecology, Yale University, vol. 22(5), pages 1080-1091, October.
    3. Rohan Sharma & Bibhas Adhikari & Tyll Krueger, 2019. "Self-Organized Corona Graphs: A Deterministic Complex Network Model With Hierarchical Structure," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-22, December.
    4. Phillips, J.C., 2014. "Fractals and self-organized criticality in proteins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 440-448.

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