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Benford Networks

Author

Listed:
  • Roeland de Kok

    (Land Consult, landConsult.de Öhinghaltweg 3 D, 77815 Bühl, Germany)

  • Giulia Rotundo

    (Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy)

Abstract

The Benford law applied within complex networks is an interesting area of research. This paper proposes a new algorithm for the generation of a Benford network based on priority rank, and further specifies the formal definition. The condition to be taken into account is the probability density of the node degree. In addition to this first algorithm, an iterative algorithm is proposed based on rewiring. Its development requires the introduction of an ad hoc measure for understanding how far an arbitrary network is from a Benford network. The definition is a semi-distance and does not lead to a distance in mathematical terms, instead serving to identify the Benford network as a class. The semi-distance is a function of the network; it is computationally less expensive than the degree of conformity and serves to set a descent condition for the rewiring. The algorithm stops when it meets the condition that either the network is Benford or the maximum number of iterations is reached. The second condition is needed because only a limited set of densities allow for a Benford network. Another important topic is assortativity and the extremes which can be achieved by constraining the network topology; for this reason, we ran simulations on artificial networks and explored further theoretical settings as preliminary work on models of preferential attachment. Based on our extensive analysis, the first proposed algorithm remains the best one from a computational point of view.

Suggested Citation

  • Roeland de Kok & Giulia Rotundo, 2022. "Benford Networks," Stats, MDPI, vol. 5(4), pages 1-14, September.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:54-947:d:930490
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    References listed on IDEAS

    as
    1. Uwe Hassler & Mehdi Hosseinkouchack, 2019. "Testing the Newcomb-Benford Law: experimental evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 26(21), pages 1762-1769, December.
    2. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    3. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    5. Erik Holst & Poul Thyregod & Peter‐Th. Wilrich, 2001. "On Conformity Testing and the Use of two Stage Procedures," International Statistical Review, International Statistical Institute, vol. 69(3), pages 419-432, December.
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