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Reliability of rank order in sampled networks

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  • P.-J. Kim
  • H. Jeong

Abstract

In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we rank individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ranking nodes from the sampled networks provide a relatively better characterisation of their ranks in the original networks than the lower-ranking nodes. A closeness-based order relationship is more reliable than any other quantity, due to the global nature of the closeness measure. In addition, we show that if access to hubs is limited during the sampling process, an increase in the sampling fraction can in fact decrease the sampling accuracy. Finally, an estimation method for assessing sampling accuracy is suggested. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • P.-J. Kim & H. Jeong, 2007. "Reliability of rank order in sampled networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(1), pages 109-114, January.
    • Handle: RePEc:spr:eurphb:v:55:y:2007:i:1:p:109-114
    DOI: 10.1140/epjb/e2007-00033-7
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    Citations

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    Cited by:

    1. Raghuram Iyengar & Christophe Van den Bulte & Thomas W. Valente, 2011. "Opinion Leadership and Social Contagion in New Product Diffusion," Marketing Science, INFORMS, vol. 30(2), pages 195-212, 03-04.
    2. Arun Advani & Bansi Malde, 2018. "Credibly Identifying Social Effects: Accounting For Network Formation And Measurement Error," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1016-1044, September.
    3. Tsugawa, Sho & Kimura, Kazuma, 2018. "Identifying influencers from sampled social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 294-303.
    4. Terrill L. Frantz & Marcelo Cataldo & Kathleen M. Carley, 2009. "Robustness of centrality measures under uncertainty: Examining the role of network topology," Computational and Mathematical Organization Theory, Springer, vol. 15(4), pages 303-328, December.
    5. Arun Advani & Bansi Malde, 2014. "Empirical methods for networks data: social effects, network formation and measurement error," IFS Working Papers W14/34, Institute for Fiscal Studies.
    6. Terrill L. Frantz & Kathleen M. Carley, 2017. "Reporting a network’s most-central actor with a confidence level," Computational and Mathematical Organization Theory, Springer, vol. 23(2), pages 301-312, June.
    7. Sho Tsugawa & Yukihiro Matsumoto & Hiroyuki Ohsaki, 2015. "On the robustness of centrality measures against link weight quantization in social networks," Computational and Mathematical Organization Theory, Springer, vol. 21(3), pages 318-339, September.

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