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Google matrix of Bitcoin network

Author

Listed:
  • Leonardo Ermann

    (Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica)

  • Klaus M. Frahm

    (Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS)

  • Dima L. Shepelyansky

    (Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS)

Abstract

We construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics including the PageRank and CheiRank probability distributions, the spectrum of eigenvalues of Google matrix and related eigenvectors. We find that the spectrum has an unusual circle-type structure which we attribute to existing hidden communities of nodes linked between their members. We show that the Gini coefficient of the transactions for the whole period is close to unity showing that the main part of wealth of the network is captured by a small fraction of users. In global the Google matrix analysis of bitcoin network gives a new understanding of the bitcoin transactions with PageRank and CheiRank characterization of sellers and buyers which are dominant not simply due to the sold/bought volume but also by taking into account if bitcoins are sold to (bought by) other important sellers (buyers).

Suggested Citation

  • Leonardo Ermann & Klaus M. Frahm & Dima L. Shepelyansky, 2018. "Google matrix of Bitcoin network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(6), pages 1-13, June.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:6:d:10.1140_epjb_e2018-80674-y
    DOI: 10.1140/epjb/e2018-80674-y
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    Citations

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    Cited by:

    1. C'elestin Coquid'e & Jos'e Lages & Dima L. Shepelyansky, 2020. "Crisis contagion in the world trade network," Papers 2002.07100, arXiv.org.
    2. Célestin Coquidé & José Lages & Dima Shepelyansky, 2020. "Crisis contagion in the world trade network," Post-Print hal-02482438, HAL.
    3. C'elestin Coquid'e & Leonardo Ermann & Jos'e Lages & D. L. Shepelyansky, 2019. "Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data," Papers 1903.01820, arXiv.org.

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    Keywords

    Statistical and Nonlinear Physics;

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