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Security of scale-free networks

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Abstract

An important property of a scale-free network which allows one to communicate between its nodes is the connectivity. From the simulation results it is known that such networks are resistant to random damage. It is also known from experiments that usually disconnecting such a graph is obtained by isolating a vertex. In this paper, we deal with a problem of isolating a vertex both experimentally and theoretically. For the theoretical results, we use the LCD model defined by Bollobás and Riordan. Among others, we prove that even after random deleting of n α vertices (m α edges) for α < (d − 1)/d, where d is the out-degree, with high probability, there are no isolated vertices in the remaining graph.

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Authors and Affiliations

  1. Department of the Theory of Algorithms and Data Security, Adam Mickiewicz University, Poznań, Poland

    M. Gała̧zka & J. Szymański

Authors
  1. M. Gała̧zka
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  2. J. Szymański
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Correspondence to M. Gała̧zka.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.

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Gała̧zka, M., Szymański, J. Security of scale-free networks. J Math Sci 182, 200–209 (2012). https://doi.org/10.1007/s10958-012-0740-4

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  • DOI: https://doi.org/10.1007/s10958-012-0740-4

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