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Ranking stability and super-stable nodes in complex networks

Author

Listed:
  • Gourab Ghoshal

    (Biology and Computer Science, Center for Complex Network Research, Northeastern University
    Harvard Medical School, and Center for Cancer Systems Biology, Dana-Farber Cancer Institute
    Media Laboratory, Massachusetts Institute of Technology)

  • Albert-László Barabási

    (Biology and Computer Science, Center for Complex Network Research, Northeastern University
    Harvard Medical School, and Center for Cancer Systems Biology, Dana-Farber Cancer Institute)

Abstract

Pagerank, a network-based diffusion algorithm, has emerged as the leading method to rank web content, ecological species and even scientists. Despite its wide use, it remains unknown how the structure of the network on which it operates affects its performance. Here we show that for random networks the ranking provided by pagerank is sensitive to perturbations in the network topology, making it unreliable for incomplete or noisy systems. In contrast, in scale-free networks we predict analytically the emergence of super-stable nodes whose ranking is exceptionally stable to perturbations. We calculate the dependence of the number of super-stable nodes on network characteristics and demonstrate their presence in real networks, in agreement with the analytical predictions. These results not only deepen our understanding of the interplay between network topology and dynamical processes but also have implications in all areas where ranking has a role, from science to marketing.

Suggested Citation

  • Gourab Ghoshal & Albert-László Barabási, 2011. "Ranking stability and super-stable nodes in complex networks," Nature Communications, Nature, vol. 2(1), pages 1-7, September.
    • Handle: RePEc:nat:natcom:v:2:y:2011:i:1:d:10.1038_ncomms1396
    DOI: 10.1038/ncomms1396
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    Cited by:

    1. Xizhe Zhang & Tianyang Lv & XueYing Yang & Bin Zhang, 2014. "Structural Controllability of Complex Networks Based on Preferential Matching," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-8, November.
    2. Xu-Cheng Yin & Bo-Wen Zhang & Xiao-Ping Cui & Jiao Qu & Bin Geng & Fang Zhou & Li Song & Hong-Wei Hao, 2016. "ISART: A Generic Framework for Searching Books with Social Information," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-27, February.
    3. Gerardo Iñiguez & Carlos Pineda & Carlos Gershenson & Albert-László Barabási, 2022. "Dynamics of ranking," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    4. Valeria Costantini & Valerio Leone Sciabolazza & Elena Paglialunga, 2023. "Network-driven positive externalities in clean energy technology production: the case of energy efficiency in the EU residential sector," The Journal of Technology Transfer, Springer, vol. 48(2), pages 716-748, April.
    5. Zhang, Jianhua & Zhou, Yu & Wang, Shuliang & Min, Qinjie, 2024. "Critical station identification and robustness analysis of urban rail transit networks based on comprehensive vote-rank algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Wang, Mingyan & Zeng, An & Cui, Xiaohua, 2022. "Collective user switching behavior reveals the influence of TV channels and their hidden community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    7. Eleanor R Brush & David C Krakauer & Jessica C Flack, 2013. "A Family of Algorithms for Computing Consensus about Node State from Network Data," PLOS Computational Biology, Public Library of Science, vol. 9(7), pages 1-17, July.

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