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Unveiling the multi-fractal structure of complex networks

Author

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  • Jalan, Sarika
  • Yadav, Alok
  • Sarkar, Camellia
  • Boccaletti, Stefano

Abstract

The fractal nature of graphs has traditionally been investigated by using the network’s nodes as the basic units. Here, instead, we propose to concentrate on the graph’s edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.

Suggested Citation

  • Jalan, Sarika & Yadav, Alok & Sarkar, Camellia & Boccaletti, Stefano, 2017. "Unveiling the multi-fractal structure of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 11-14.
    • Handle: RePEc:eee:chsofr:v:97:y:2017:i:c:p:11-14
    DOI: 10.1016/j.chaos.2017.01.021
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    Citations

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    Cited by:

    1. Sato, Yoshihiro & Mizukami, Yuka & Takeda, Mariko & Okubo, Kazuya & Kobayashi, Ryota & Munakata, Fumio, 2021. "Quantitative evaluation of morphological characteristics of self-assembled aggregates using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Panigrahy, Chinmaya & Seal, Ayan & Mahato, Nihar Kumar & Bhattacharjee, Debotosh, 2019. "Differential box counting methods for estimating fractal dimension of gray-scale images: A survey," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 178-202.
    3. Sato, Yoshihiro & Munakata, Fumio, 2022. "Morphological characteristics of self-assembled aggregate textures using multifractal analysis: Interpretation of Multifractal τ(q) Using Simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    4. Moreno-Pulido, Soledad & Pavón-Domínguez, Pablo & Burgos-Pintos, Pedro, 2021. "Temporal evolution of multifractality in the Madrid Metro subway network," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Deniz, Ali & Çakmak, Gökçe, 2018. "On the smallest disks enclosing graph-directed fractals," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 483-490.

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    Keywords

    Fractal dimension; Complex networks;

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