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Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network

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  • Hirokazu Kawamoto
  • Hideki Takayasu
  • Henrik Jeldtoft Jensen
  • Misako Takayasu

Abstract

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.

Suggested Citation

  • Hirokazu Kawamoto & Hideki Takayasu & Henrik Jeldtoft Jensen & Misako Takayasu, 2015. "Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-16, April.
    • Handle: RePEc:plo:pone00:0119979
    DOI: 10.1371/journal.pone.0119979
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    References listed on IDEAS

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    5. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "The Structure and Evolution of Buyer-Supplier Networks," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-10, July.
    6. Mizuno, Takayuki & Souma, Wataru & Watanabe, Tsutomu, 2014. "The Structure and Evolution of Buyer-Supplier Networks," Working Paper Series 27, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
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    Cited by:

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    2. Zhukov, Dmitry & Khvatova, Tatiana & Lesko, Sergey & Zaltcman, Anastasia, 2018. "Managing social networks: Applying the percolation theory methodology to understand individuals' attitudes and moods," Technological Forecasting and Social Change, Elsevier, vol. 129(C), pages 297-307.
    3. Tsouchnika, Maria & Smolyak, Alex & Argyrakis, Panos & Havlin, Shlomo, 2022. "Patent collaborations: From segregation to globalization," Journal of Informetrics, Elsevier, vol. 16(1).

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