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Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks

Author

Listed:
  • Kitsak, Maksim
  • Havlin, Shlomo
  • Paul, Gerald
  • Riccaboni, Massimo
  • Pammolli, Fabio
  • Stanley, H. Eugene

Abstract

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution P(C) ~ C^δ. We find that for non-fractal scale-free networks δ = -2, and for fractal scale-free networks δ = -2 + 1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N = 6776), yeast (N = 1458), WWW (N = 2526), and a sample of Internet network at AS level (N = 20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length ℓ*, separating fractal and non-fractal regimes, scales with dimension dB of the network as p−1/dB, where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.

Suggested Citation

  • Kitsak, Maksim & Havlin, Shlomo & Paul, Gerald & Riccaboni, Massimo & Pammolli, Fabio & Stanley, H. Eugene, 2007. "Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks," MPRA Paper 15907, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15907
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    References listed on IDEAS

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    1. Orsenigo, L. & Pammolli, F. & Riccaboni, Massimo, 2001. "Technological change and network dynamics: Lessons from the pharmaceutical industry," Research Policy, Elsevier, vol. 30(3), pages 485-508, March.
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    Cited by:

    1. Sun, Lina & Huang, Ning & Li, Ruiying & Bai, Yanan, 2019. "A new fractal reliability model for networks with node fractal growth and no-loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 699-707.
    2. Huiling Zhang & Yilin Shen & My T. Thai, 2016. "Robustness of power-law networks: its assessment and optimization," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 696-720, October.
    3. Huang, Da-Wen & Yu, Zu-Guo & Anh, Vo, 2017. "Multifractal analysis and topological properties of a new family of weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 695-705.
    4. Mahyar, Hamidreza & Hasheminezhad, Rouzbeh & Ghalebi K., Elahe & Nazemian, Ali & Grosu, Radu & Movaghar, Ali & Rabiee, Hamid R., 2018. "Compressive sensing of high betweenness centrality nodes in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 166-184.
    5. Georgi Yordanov Georgiev & Atanu Chatterjee & Germano Iannacchione, 2017. "Exponential Self-Organization and Moore’s Law: Measures and Mechanisms," Complexity, Hindawi, vol. 2017, pages 1-9, January.

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    Keywords

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    JEL classification:

    • L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology; Plastics
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • L60 - Industrial Organization - - Industry Studies: Manufacturing - - - General
    • L00 - Industrial Organization - - General - - - General
    • L63 - Industrial Organization - - Industry Studies: Manufacturing - - - Microelectronics; Computers; Communications Equipment

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