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Contagion in Bitcoin networks

Author

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  • Célestin Coquidé

    (UTINAM - Univers, Théorie, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213) - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • José Lages

    (UTINAM - Univers, Théorie, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213) - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Dima Shepelyansky

    (ICQ - Cohérence Quantique (LPT) - LPT - Laboratoire de Physique Théorique - IRSAMC - Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique, LPT - Laboratoire de Physique Théorique - IRSAMC - Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique)

Abstract

We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold $\kappa$. We find that the phase transition takes place for $\kappa0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $\kappa_c$ the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks.

Suggested Citation

  • Célestin Coquidé & José Lages & Dima Shepelyansky, 2019. "Contagion in Bitcoin networks," Post-Print hal-02147768, HAL.
    • Handle: RePEc:hal:journl:hal-02147768
    DOI: 10.1007/978-3-030-36691-9_18
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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.

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