Journal of information and communication convergence engineering

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Topology Characteristics and Generation Models of Scale-Free Networks

  • Lee, Kang Won (Department of Industrial and Information Systems Engineering, Seoul National University of Science and Technology) ;
  • Lee, Ji Hwan (Department of Industrial and Information Systems Engineering, Seoul National University of Science and Technology)
  • Received : 2021.08.30
  • Accepted : 2021.10.05
  • Published : 2021.12.31
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Abstract

The properties of a scale-free network are little known; its node degree following a power-law distribution is among its few known properties. By selecting real-field scale-free networks from a network dataset and comparing them to other networks, such as random and non-scale-free networks, the topology characteristics of scale-free networks are identified. The assortative coefficient is identified as a key metric of a scale-free network. It is also identified that most scale-free networks have negative assortative coefficients. Traditional generation models of scale-free networks are evaluated based on the identified topology characteristics. Most representative models, such as BA and Holme&Kim, are not effective in generating real-field scale-free networks. A link-rewiring method is suggested that can control the assortative coefficient while preserving the node degree sequence. Our analysis reveals that it is possible to effectively reproduce the assortative coefficients of real-field scale-free networks through link-rewiring.

Keywords

Acknowledgement

This research was supported by the Seoul National University of Science and Technology research funds.

References

  1. A. Mislove, M. Marcon, K. P. Gummadi, P. Druschel, and B. Bhattacharjee, "Measurement and analysis of online social networks," in Proceedings of 7th ACM SIGCOMM Conference on Internet Measurement, pp. 29-42, 2007. DOI: 10.1145/1298306.1298311.
  2. R. Khanin and E. Wit, "How scale-free are biological networks," Journal of Computational Biology, vol. 13, no. 3, pp. 810-818, 2006. DOI: 10.1089/cmb.2006.13.810.
  3. K. W. Lee, "On-line social network generation model," Journal of the Korea Institute of Information and Communication Engineering, vol. 24, no. 7, pp. 914-924, 2020. DOI: 10.6109/jkiice.2020.24.7.914.
  4. R. Albert, "Scale-free networks in cell biology," Journal of Cell Science, vol. 118, pp. 4947-4957, 2005. DOI: 10.1242/jcs.02714.
  5. R. Cohen, K. Erez, D. Avraham, and S. Havlin, "Resilience of the Internet to random breakdowns," Physical Review Letters, vol. 85, no. 21, pp. 4626-4628, 2000. DOI: 10.1103/PhysRevLett.85.4626.
  6. K. W. Lee and J. S. Lee, "Power-law of node degree distribution and information diffusion process," The Journal of Korean Institute of Communications and Information Science, vol. 44, no. 10, pp. 1866-1877, 2019. DOI: 10.7840/kics.2019.44.10.1866.
  7. Z. Jing, T. Lin, Y. Hong, L. J. Hua, C. Z. Wei, and L. Y. Xue, "The effects of degree correlations on network topologies and robustness," Chinese Physics, vol. 16, no. 12, pp. 1-11, 2007. DOI: 10.1088/1009-1963/16/12/004.
  8. A. Barabasi and R. Albert, "Emergence of scaling in random networks," Science, vol. 286, no. 5439, pp. 509-512, 1999. DOI: 10.1126/science.286.5439.509.
  9. P. Holme and B. J. Kim, "Growing scale-free networks with tunable clustering," Physical Review E, vol. 65, no. 2, pp. 026107.1- 026107.4, 2002, DOI: 10.1103/PhysRevE.65.026107.
  10. A. Vazquez, R. Pastor-Satorras, and A. Vespignani, "Large-scale topological and dynamical properties of the Internet," Physical Review E, vol. 64, no. 6, pp. 66-130, 2002. DOI: 10.1103/PhysRevE.65.066130.
  11. F. Gursoy and B. Badur, "A Community-aware network growth model for synthetic social network generation," in Proceedings of the 5th International Management Information Systems Conference, pp. 1-8, 2019. DOI: 10.6084/m9.figshare.7582082.
  12. Y. Liu, L. Li, H. Wang, C. Sun, X. Chen, J. He, and Y. Jiang, "The competition of homophily and popularity in growing and evolving social networks," Scientific Reports, vol. 8, no. 1, pp. 1-16, 2018. DOI: 10.1038/s41598-018-33409-8.
  13. D. Tsiotas, "Detecting different topologies immanent in scale-free networks with the same degree distribution," in Proceedings of the National Academy of Sciences, vol. 116, no. 14, pp. 6701-6706, 2019. DOI: 10.1073/pnas.1816842116.
  14. J. Leskovec and A. Krevl, Standford large network dataset collection, 2014, [Online] Available: http://snap.standford.edu/data.
  15. R. A. Rossi and N. K. Ahmed, The Network data Repository with Interactive Graph Analytics and visualization, 2015, [Online] Available: http://networkrepository.com.
  16. A. Clauset, E. Tucker, and M. Sainz, The Colorado index of complex networks, 2016, [Online] Available: http://icon.colorado.edu/.
  17. A. D. Broido and A. Clauset, "Scale-free networks are rare," Nature Communications, vol. 10, pp. 1-11, 2019. DOI: 10.1038/s41467-019-08746-5.
  18. B. Kantarci and V. Labatut, "Classification of complex networks based on topological properties," in 2013 International Conference on Cloud and Green Computing, pp. 297-304, 2013. DOI: 10.1109/CGC.2013.54.
  19. P. Erdos and A. Renyi, "On random graphs I.," Publicationes Mathematicae Debresen, vol. 6, pp. 290-297, 1959.
  20. M. E. J. Newman, "Detecting community structure in networks," The European Physical Journal B, vol. 38, pp. 321-330, 2004. DOI: 10.1140/epjb/e2004-00124-y.
  21. M. E. J. Newman, "Modularity and community structure in netoworks," in Proceedings of National Academic Science, vol. 103, no. 23, pp. 8577-8582, 2006. DOI: 10.1073/pnas.0601602103.