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A new deterministic complex network model with hierarchical structure

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  • Chen, Mu
  • Yu, Boming
  • Xu, Peng
  • Chen, Jun

Abstract

We introduce a new simple pseudo tree-like network model, deterministic complex network (DCN). The proposed DCN model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of ‘skipping the levels’, which is ubiquitous in social networks. Our results indicate that the DCN model has a rather small average path length and large clustering coefficient, leading to the small-world effect. Strikingly, our DCN model obeys a discrete power-law degree distribution P(k)∝k−γ, with exponent γ approaching 1.0. We also discover that the relationship between the clustering coefficient and degree follows the scaling law C(k)∼k−1, which quantitatively determines the DCN's hierarchical structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:707-717
    DOI: 10.1016/j.physa.2007.07.032
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    References listed on IDEAS

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    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    2. 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.
    3. 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.
    4. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
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    Cited by:

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    2. Hollingshad, Nicholas W. & Turalska, Malgorzata & Allegrini, Paolo & West, Bruce J. & Grigolini, Paolo, 2012. "A new measure of network efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1894-1899.
    3. Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    4. 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.

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