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Modeling complex networks with self-similar outerplanar unclustered graphs

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  • Comellas, Francesc
  • Miralles, Alicia

Abstract

This paper introduces a family of modular, self-similar, small-world graphs with clustering zero. Relevant properties of this family are comparable to those of some networks associated with technological systems with a low clustering, like the power grid or some electronic circuits. Moreover, the graphs are outerplanar and it is know that many algorithms that are NP-complete for general graphs perform polynomial in outerplanar graphs. Therefore the graphs constitute a good mathematical model for these systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:11:p:2227-2233
    DOI: 10.1016/j.physa.2009.02.004
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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.
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    3. Zhang, Zhongzhi & Zhou, Shuigeng & Shen, Zhen & Guan, Jihong, 2007. "From regular to growing small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 765-772.
    4. Zhang, Zhongzhi & Rong, Lili & Guo, Chonghui, 2006. "A deterministic small-world network created by edge iterations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 567-572.
    5. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    6. 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.
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    Citations

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    Cited by:

    1. Comellas, Francesc & Miralles, Alícia & Liu, Hongxiao & Zhang, Zhongzhi, 2013. "The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2803-2806.
    2. Knor, Martin & Škrekovski, Riste, 2013. "Deterministic self-similar models of complex networks based on very symmetric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4629-4637.
    3. Xiao, Wenjun & Lin, Longxin & Chen, Guanrong, 2015. "Vertex-degree sequences in complex networks: New characteristics and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 437-441.
    4. Yinhu Zhai & Jia-Bao Liu & Shaohui Wang, 2017. "Structure Properties of Koch Networks Based on Networks Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-7, March.
    5. Liao, Yunhua & Fang, Aixiang & Hou, Yaoping, 2013. "The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4584-4593.
    6. 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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