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Blackmail propagation on small-world networks

Author

Listed:
  • Shao, Zhi-Gang
  • Jian-Ping Sang,
  • Zou, Xian-Wu
  • Tan, Zhi-Jie
  • Jin, Zhun-Zhi

Abstract

The dynamics of the blackmail propagation model based on small-world networks is investigated. It is found that for a given transmitting probability λ the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases. The transition takes place at the critical network randomness pc=1/N, where N is the total number of nodes in the network. For a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability λ increases. The transition occurs at the critical transmitting probability λc=1/〈k〉, where 〈k〉 is the average number of the nearest neighbors. The present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks.

Suggested Citation

  • Shao, Zhi-Gang & Jian-Ping Sang, & Zou, Xian-Wu & Tan, Zhi-Jie & Jin, Zhun-Zhi, 2005. "Blackmail propagation on small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 662-670.
    • Handle: RePEc:eee:phsmap:v:351:y:2005:i:2:p:662-670
    DOI: 10.1016/j.physa.2004.11.063
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    References listed on IDEAS

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    1. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
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