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A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks

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  • de Sá, Luiz Alberto Pereira
  • Zielinski, Kallil M.C.
  • Rodrigues, Érick Oliveira
  • Backes, André R.
  • Florindo, João B.
  • Casanova, Dalcimar

Abstract

A complex network presents many topological features which characterize its behavior and dynamics. This characterization is an essential aspect of complex networks analysis and can be performed using several measures, including the fractal dimension. Originally the fractal dimension measures the complexity of an object in a Euclidean space, and the most common methods in the literature to estimate that dimension are box-counting, mass-radius, and Bouligand-Minkowski. However, networks are not Euclidean objects, so that these methods require some adaptation to measure the fractal dimension in this context. The literature presents some adaptations for methods like box-counting and mass-radius. However, there is no known adaptation developed for the Bouligand-Minkowski method. In this way, we propose an adaptation of the Bouligand-Minkowski to measure complex networks’ fractal dimension. We compare our proposed method with others, and we also explore the application of the proposed method in a classification task of complex networks that confirmed its promising potential.

Suggested Citation

  • de Sá, Luiz Alberto Pereira & Zielinski, Kallil M.C. & Rodrigues, Érick Oliveira & Backes, André R. & Florindo, João B. & Casanova, Dalcimar, 2022. "A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001059
    DOI: 10.1016/j.chaos.2022.111894
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
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    5. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
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    Cited by:

    1. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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