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An Exact and an Approximation Method to Compute the Degree Distribution of Inhomogeneous Random Graph Using Poisson Binomial Distribution

Author

Listed:
  • Róbert Pethes

    (Physiological Controls Research Center, Óbuda University, 1034 Budapest, Hungary)

  • Levente Kovács

    (Physiological Controls Research Center, Óbuda University, 1034 Budapest, Hungary)

Abstract

Inhomogeneous random graphs are commonly used models for complex networks where nodes have varying degrees of connectivity. Computing the degree distribution of such networks is a fundamental problem and has important applications in various fields. We define the inhomogeneous random graph as a random graph model where the edges are drawn independently and the probability of a link between any two vertices can be different for each node pair. In this paper, we present an exact and an approximation method to compute the degree distribution of inhomogeneous random graphs using the Poisson binomial distribution. The exact algorithm utilizes the DFT-CF method to compute the distribution of a Poisson binomial random variable. The approximation method uses the Poisson, binomial, and Gaussian distributions to approximate the Poisson binomial distribution.

Suggested Citation

  • Róbert Pethes & Levente Kovács, 2023. "An Exact and an Approximation Method to Compute the Degree Distribution of Inhomogeneous Random Graph Using Poisson Binomial Distribution," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1441-:d:1099063
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    References listed on IDEAS

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    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    2. Hong, Yili, 2013. "On computing the distribution function for the Poisson binomial distribution," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 41-51.
    3. Ehm, Werner, 1991. "Binomial approximation to the Poisson binomial distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 7-16, January.
    4. J. Buhl & J. Gautrais & N. Reeves & R. V. Solé & S. Valverde & P. Kuntz & G. Theraulaz, 2006. "Topological patterns in street networks of self-organized urban settlements," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(4), pages 513-522, February.
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