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Complex networks constructed from irrational number sequences

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  • Chen, Chen
  • Lu, Jun-an
  • Wu, Xiaoqun

Abstract

In this paper, we construct (d,r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r=0,1,…,d−1), and the undirected edges indicate the adjacency between two consecutive groups. (3,r) and (4,r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

Suggested Citation

  • Chen, Chen & Lu, Jun-an & Wu, Xiaoqun, 2010. "Complex networks constructed from irrational number sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2654-2662.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:13:p:2654-2662
    DOI: 10.1016/j.physa.2010.02.033
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    References listed on IDEAS

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    Cited by:

    1. Hu, Xiaohua & Niu, Min, 2023. "Horizontal visibility graphs mapped from multifractal trinomial measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

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