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High-dimensional random Apollonian networks

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  • Zhang, Zhongzhi
  • Rong, Lili
  • Comellas, Francesc

Abstract

We propose a simple algorithm which produces a new category of networks, high-dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We estimate also analytically that the average path length of the networks increases at most logarithmically with the number of vertices.

Suggested Citation

  • Zhang, Zhongzhi & Rong, Lili & Comellas, Francesc, 2006. "High-dimensional random Apollonian networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 610-618.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:610-618
    DOI: 10.1016/j.physa.2005.09.042
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    References listed on IDEAS

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    1. Comellas, Francesc & Sampels, Michael, 2002. "Deterministic small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 231-235.
    2. 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.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Wang, Xiaomin & Yao, Bing, 2020. "Two cumulative distributions for scale-freeness of dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    3. Hiro Ito, 2019. "What Graph Properties Are Constant-Time Testable?," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 101-121, October.
    4. Prettejohn, Brenton J. & Berryman, Matthew J. & McDonnell, Mark D., 2013. "A model of the effects of authority on consensus formation in adaptive networks: Impact on network topology and robustness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 857-868.
    5. Miralles, Alicia & Comellas, Francesc & Chen, Lichao & Zhang, Zhongzhi, 2010. "Planar unclustered scale-free graphs as models for technological and biological networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1955-1964.

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