IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v465y2017icp141-152.html
   My bibliography  Save this article

Parameter specification for the degree distribution of simulated Barabási–Albert graphs

Author

Listed:
  • Mohd-Zaid, Fairul
  • Kabban, Christine M. Schubert
  • Deckro, Richard F.
  • White, Edward D.

Abstract

The degree distribution of a simulated Barabási–Albert graph under linear preferential attachment is investigated. Specifically, the parameters of the power law distribution are estimated and compared against the theoretical values derived using mean field theory. Least squares method and MLE-nonparametric method were utilized to estimate the distribution parameters on 1000 simulated Barabási–Albert graphs for edge parameter m∈{2,4,6} and size n∈{2k:k=5,6,…,14,15}. Goodness of fit metrics were computed on a second set of simulated graphs for the median of the estimated parameters and other hypothetical values for the distribution parameters. The results suggest that the distribution of the parameters from simulated graphs are significantly different from the theoretical distribution and is also dependent on m. Further results confirm the finding that the parameter of the power law distribution, β, increases as m increases.

Suggested Citation

  • Mohd-Zaid, Fairul & Kabban, Christine M. Schubert & Deckro, Richard F. & White, Edward D., 2017. "Parameter specification for the degree distribution of simulated Barabási–Albert graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 141-152.
    • Handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:141-152
    DOI: 10.1016/j.physa.2016.07.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116304551
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.07.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Ping & Zhang, Jie & Small, Michael, 2011. "Emergence of scaling and assortative mixing through altruism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2192-2197.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    3. Zhang, Linjun & Small, Michael & Judd, Kevin, 2015. "Exactly scale-free scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 182-197.
    4. Wang, Xiangrong & Trajanovski, Stojan & Kooij, Robert E. & Van Mieghem, Piet, 2016. "Degree distribution and assortativity in line graphs of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 343-356.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    2. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    3. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    4. Baek, Seung Ki & Kim, Tae Young & Kim, Beom Jun, 2008. "Testing a priority-based queue model with Linux command histories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3660-3668.
    5. Freddy Hernán Cepeda López, 2008. "La topología de redes como herramienta de seguimiento en el Sistema de Pagos de Alto Valor en Colombia," Borradores de Economia 513, Banco de la Republica de Colombia.
    6. Chung-Yuan Huang & Chuen-Tsai Sun & Hsun-Cheng Lin, 2005. "Influence of Local Information on Social Simulations in Small-World Network Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-8.
    7. Xue Guo & Hu Zhang & Tianhai Tian, 2019. "Multi-Likelihood Methods for Developing Stock Relationship Networks Using Financial Big Data," Papers 1906.08088, arXiv.org.
    8. Chang, Chia-ling & Chen, Shu-heng, 2011. "Interactions in DSGE models: The Boltzmann-Gibbs machine and social networks approach," Economics Discussion Papers 2011-25, Kiel Institute for the World Economy (IfW Kiel).
    9. Lin, Yi & Zhang, Jianwei & Yang, Bo & Liu, Hong & Zhao, Liping, 2019. "An optimal routing strategy for transport networks with minimal transmission cost and high network capacity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 551-561.
    10. Stefano Breschi & Lucia Cusmano, 2002. "Unveiling the Texture of a European Research Area: Emergence of Oligarchic Networks under EU Framework Programmes," KITeS Working Papers 130, KITeS, Centre for Knowledge, Internationalization and Technology Studies, Universita' Bocconi, Milano, Italy, revised Jul 2002.
    11. He, Xuan & Zhao, Hai & Cai, Wei & Li, Guang-Guang & Pei, Fan-Dong, 2015. "Analyzing the structure of earthquake network by k-core decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 34-43.
    12. Huang, Huilin, 2009. "The degree sequences of an asymmetrical growing network," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 420-425, February.
    13. Gianluca Carnabuci, 2013. "The distribution of technological progress," Empirical Economics, Springer, vol. 44(3), pages 1143-1154, June.
    14. Zhengzheng Pan, 2012. "Opinions and Networks: How Do They Effect Each Other," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 157-171, February.
    15. 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.
    16. Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    17. Zhang, Lan & Huang, Changwei, 2023. "Preferential selection to promote cooperation on degree–degree correlation networks in spatial snowdrift games," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    18. Feng Xie & David Levinson, 2009. "Modeling the Growth of Transportation Networks: A Comprehensive Review," Networks and Spatial Economics, Springer, vol. 9(3), pages 291-307, September.
    19. Srayan Datta & Eytan Adar, 2018. "A generative model for scientific concept hierarchies," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-19, February.
    20. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:141-152. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.