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Deterministic walks in random networks: an application to thesaurus graphs

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  • Kinouchi, O
  • Martinez, A.S
  • Lima, G.F
  • Lourenço, G.M
  • Risau-Gusman, S

Abstract

In a landscape composed of N randomly distributed sites in Euclidean space, a walker (“tourist”) goes to the nearest one that has not been visited in the last τ steps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p. The tourist walk presents a simple scaling with respect to τ and can be performed in a wide range of networks that can be viewed as ordinal neighborhood graphs. As an example, we show that graphs defined by thesaurus dictionaries share some of the statistical properties of low-dimensional (d=2) Euclidean graphs and are easily distinguished from random link networks which correspond to the d→∞ limit. This approach furnishes complementary information to the usual clustering coefficient and mean minimum separation length.

Suggested Citation

  • Kinouchi, O & Martinez, A.S & Lima, G.F & Lourenço, G.M & Risau-Gusman, S, 2002. "Deterministic walks in random networks: an application to thesaurus graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 665-676.
    • Handle: RePEc:eee:phsmap:v:315:y:2002:i:3:p:665-676
    DOI: 10.1016/S0378-4371(02)00972-X
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. G. M. Viswanathan & Sergey V. Buldyrev & Shlomo Havlin & M. G. E. da Luz & E. P. Raposo & H. Eugene Stanley, 1999. "Optimizing the success of random searches," Nature, Nature, vol. 401(6756), pages 911-914, October.
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    Cited by:

    1. Li, Jianyu & Zhou, Jie & Luo, Xiaoyue & Yang, Zhanxin, 2012. "Chinese lexical networks: The structure, function and formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5254-5263.
    2. Li, Jianyu & Zhou, Jie, 2007. "Chinese character structure analysis based on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 629-638.
    3. de Jesus Holanda, Adriano & Torres Pisa, Ivan & Kinouchi, Osame & Souto Martinez, Alexandre & Eduardo Seron Ruiz, Evandro, 2004. "Thesaurus as a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 530-536.
    4. Amancio, D.R. & Nunes, M.G.V. & Oliveira, O.N. & Pardo, T.A.S. & Antiqueira, L. & da F. Costa, L., 2011. "Using metrics from complex networks to evaluate machine translation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 131-142.

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