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Robustness of centrality measures under uncertainty: Examining the role of network topology

Author

Listed:
  • Terrill L. Frantz

    (Carnegie Mellon University)

  • Marcelo Cataldo

    (Two North Shore Center)

  • Kathleen M. Carley

    (Carnegie Mellon University)

Abstract

This study investigates the topological form of a network and its impact on the uncertainty entrenched in descriptive measures computed from observed social network data, given ubiquitous data-error. We investigate what influence a network’s topology, in conjunction with the type and amount of error, has on the ability of a measure, derived from observed data, to correctly approximate the same of the ground-truth network. By way of a controlled experiment, we reveal the differing effect that observation error has on measures of centrality and local clustering across several network topologies: uniform random, small-world, core-periphery, scale-free, and cellular. Beyond what is already known about the impact of data uncertainty, we found that the topology of a social network is, indeed, germane to the accuracy of these measures. In particular, our experiments show that the accuracy of identifying the prestigious, or key, actors in a network—according observed data—is considerably predisposed by the topology of the ground-truth network.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comaot:v:15:y:2009:i:4:d:10.1007_s10588-009-9063-5
    DOI: 10.1007/s10588-009-9063-5
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    Cited by:

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    2. Virginie Masson & Kelsey Wilkins, 2013. "The Small World of 9/11 and the Implications for Network Dismantlement Strategies," School of Economics and Public Policy Working Papers 2013-08, University of Adelaide, School of Economics and Public Policy.
    3. Andrea Landherr & Bettina Friedl & Julia Heidemann, 2010. "A Critical Review of Centrality Measures in Social Networks," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 2(6), pages 371-385, December.
    4. Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.
    5. Jianjun Lu & Shozo Tokinaga, 2013. "Analysis of cluster formations on planer cells based on genetic programming," Computational and Mathematical Organization Theory, Springer, vol. 19(4), pages 426-445, December.
    6. Zhang, Xin-Jie & Tang, Yong & Xiong, Jason & Wang, Wei-Jia & Zhang, Yi-Cheng, 2020. "Ranking game on networks: The evolution of hierarchical society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Yu Zhang & Yu Wu, 2012. "How behaviors spread in dynamic social networks," Computational and Mathematical Organization Theory, Springer, vol. 18(4), pages 419-444, December.
    8. 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.
    9. Dunn, Adam G. & Westbrook, Johanna I., 2011. "Interpreting social network metrics in healthcare organisations: A review and guide to validating small networks," Social Science & Medicine, Elsevier, vol. 72(7), pages 1064-1068, April.
    10. Stella, Massimo, 2020. "Multiplex networks quantify robustness of the mental lexicon to catastrophic concept failures, aphasic degradation and ageing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    11. 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.
    12. 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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