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The Degree Profile in Some Classes of Random Graphs that Generalize Recursive Trees

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  • Hosam M. Mahmoud

    (The George Washington University)

Abstract

We study the degree profile for a number of classes of random graphs that arise as generalizations of recursive trees, including random circuits and random recursive trees endowed with the power of choice. We investigate the distribution of the degrees of nodes that appear in various stages of the insertion process in each of these graph types. For these classes, we will see phase transitions in degrees depending on the stage—early stages are associated with normal distributions, intermediate stages are associated with the Poisson distribution and in the late stages the degrees become degenerate.

Suggested Citation

  • Hosam M. Mahmoud, 2014. "The Degree Profile in Some Classes of Random Graphs that Generalize Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 527-538, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-012-9312-9
    DOI: 10.1007/s11009-012-9312-9
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    References listed on IDEAS

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    1. Hosam M. Mahmoud, 2010. "The Power of Choice in the Construction of Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 763-773, December.
    2. R. M. D'Souza & P. L. Krapivsky & C. Moore, 2007. "The power of choice in growing trees," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 59(4), pages 535-543, October.
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    Cited by:

    1. Panpan Zhang & Hosam M. Mahmoud, 2020. "On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 625-645, June.
    2. Panpan Zhang, 2023. "On Several Properties of A Class of Hybrid Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-20, March.

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