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A small world network of prime numbers

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  • Chandra, Anjan Kumar
  • Dasgupta, Subinay

Abstract

According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers: n=p+q. We construct a network where each node is a prime number and corresponding to every even number n, we put a link between the component primes p and q. In most cases, an even number can be broken up in many ways, and then we chose one decomposition with a probability |p-q|α. Through computation of average shortest distance and clustering coefficient, we conclude that for α>-1.8 the network is of small world type and for α<-1.8 it is of regular type. We also present a theoretical justification for such behaviour.

Suggested Citation

  • Chandra, Anjan Kumar & Dasgupta, Subinay, 2005. "A small world network of prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 436-446.
    • Handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:436-446
    DOI: 10.1016/j.physa.2005.02.089
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    Cited by:

    1. Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    2. Yinhu Zhai & Jia-Bao Liu & Shaohui Wang, 2017. "Structure Properties of Koch Networks Based on Networks Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-7, March.
    3. Frank Emmert-Streib, 2013. "Structural Properties and Complexity of a New Network Class: Collatz Step Graphs," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-14, February.
    4. Li, Yinwei & Jiang, Guo-Ping & Wu, Meng & Song, Yu-Rong & Wang, Haiyan, 2021. "Undirected Congruence Model: Topological characteristics and epidemic spreading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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