Communities and classes in symmetric fractals

Małgorzata J. Krawczyk ()
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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

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 03, 1-16

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.

Keywords: Fractals; communities; overlapping; networks; classes of nodes; 05.45.Df; 07.05.Tp (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115500254

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