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Planar unclustered scale-free graphs as models for technological and biological networks

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  • Miralles, Alicia
  • Comellas, Francesc
  • Chen, Lichao
  • Zhang, Zhongzhi

Abstract

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases — usually associated with topological restrictions — their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular several families of technological and biological networks, and in the design of new practical communication algorithms in relation to their dynamical processes. They can also help understanding the underlying mechanisms that have produced their particular structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:9:p:1955-1964
    DOI: 10.1016/j.physa.2009.12.056
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    References listed on IDEAS

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    1. 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.
    2. 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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    4. 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.
    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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