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Self-Organized Corona Graphs: A Deterministic Complex Network Model With Hierarchical Structure

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  • ROHAN SHARMA

    (Department of Computer Science Engineering, Bennett University, India)

  • BIBHAS ADHIKARI

    (Department of Mathematics, Indian Institute of Technology, Kharagpur, India)

  • TYLL KRUEGER

    (Wroclaw University of Technology, Poland)

Abstract

In this paper, we propose a self-organization mechanism for newly appeared nodes during the formation of corona graphs that define a hierarchical pattern in the resulting corona graphs and we call it self-organized corona graphs (SoCG). We show that the degree distribution of SoCG follows power-law in its tail with power-law exponent approximately 2. We also show that the diameter is less equal to 4 for SoCG defined by any seed graph and for certain seed graphs, the diameter remains constant during its formation. We derive lower bounds of clustering coefficients of SoCG defined by certain seed graphs. Thus, the proposed SoCG can be considered as a growing network generative model which is defined by using the corona graphs and a self-organization process such that the resulting graphs are scale-free small-world highly clustered growing networks. The SoCG defined by a seed graph can also be considered as a network with a desired motif which is the seed graph itself.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:acsxxx:v:22:y:2019:i:06:n:s021952591950019x
    DOI: 10.1142/S021952591950019X
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    References listed on IDEAS

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    1. 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.
    2. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
    3. 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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