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Branches in scale-free trees

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Abstract

In the paper the scale-free (preferential attachment) model of a random recursive tree is considered. We deal with the size and the distribution of vertex degrees in the kth branch of such a tree (which is the subtree rooted at vertex labeled k). A comparison of these results with analogous results for the whole tree shows that the k-branch of a scale-free tree can be considered as a scale-free tree itself with the number of vertices being random variables.

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Author information

Authors and Affiliations

  1. Poznań University of Technology, Department of Mathematics, Poznań, Poland

    M. Dondajewski

  2. Adam Mickiewicz University, Department of Discrete Mathematics, Poznań, Poland

    J. Szymański

Authors
  1. M. Dondajewski
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  2. J. Szymański
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Corresponding author

Correspondence to M. Dondajewski.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 63, Optimal Control, 2009.

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Dondajewski, M., Szymański, J. Branches in scale-free trees. J Math Sci 161, 961–968 (2009). https://doi.org/10.1007/s10958-009-9615-8

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  • DOI: https://doi.org/10.1007/s10958-009-9615-8

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