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Growing network: Models following nonlinear preferential attachment rule

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  • Zadorozhnyi, V.N.
  • Yudin, E.B.

Abstract

We investigate the preferential attachment graphs proceeding from the following two assumptions. The first one: the probability that a new vertex connects to a vertex i is proportional to an arbitrary nonnegative function f of a vertex degree k. The second assumption: a new vertex can have a random number of edges. We derive formulas for any f to determine the vertex degree distribution {Qk} in generated graphs. The inverse problem is solved: we have obtained formulas, that allow from a given distribution {Qk} to determine f (the problem of a model calibration). The formulas allowing for any f to calculate the joint distribution of vertex degrees at the ends of randomly selected edge are also obtained. Some other results are presented in the paper.

Suggested Citation

  • Zadorozhnyi, V.N. & Yudin, E.B., 2015. "Growing network: Models following nonlinear preferential attachment rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 111-132.
    • Handle: RePEc:eee:phsmap:v:428:y:2015:i:c:p:111-132
    DOI: 10.1016/j.physa.2015.01.052
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    Citations

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    Cited by:

    1. Li, Bo & Sun, Duoyong & Bai, Guanghan, 2017. "Empirical research on evolutionary behavior of covert network with preference measurement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 33-43.
    2. Safaei, F. & Yeganloo, H. & Akbar, R., 2020. "Robustness on topology reconfiguration of complex networks: An entropic approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 379-409.
    3. Liao, Fuxuan & Hayashi, Yukio, 2022. "Emergence of robust and efficient networks in a family of attachment models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).

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