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Communities and classes in symmetric fractals

Author

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  • Małgorzata J. Krawczyk

    (Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland)

Abstract

Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analyzed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.

Suggested Citation

  • Małgorzata J. Krawczyk, 2015. "Communities and classes in symmetric fractals," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-16.
    • Handle: RePEc:wsi:ijmpcx:v:26:y:2015:i:03:n:s0129183115500254
    DOI: 10.1142/S0129183115500254
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