Exploring the Mesoscopic Structure of Bitcoin During its First Decade of Life

Authors

  • Nicolò Vallarano Department of Informatics and UZH Blockchain Center, University of Zurich, Switzerland
  • Tiziano Squartini IMT School for Advanced Studies Lucca and INDAM - National Institute for Advanced Mathematics, Rome, Italy
  • Claudio J. Tessone Department of Informatics, and UZH Blockchain Center, University of Zurich, Switzerland

DOI:

https://doi.org/10.5195/ledger.2024.335

Keywords:

networks, bitcoin, transactions, complex systems

Abstract

The public availability of the entire history of Bitcoin transactions opens up the unprecedented possibility of studying this system at the desired level of detail. Our contribution is intended to analyse the mesoscopic properties of the Bitcoin User Network (BUN) during the first half of its history, i.e., across the years 2011-2018. What emerges from our analysis is that the BUN is a core-periphery structure with a certain degree of “bow-tieness”, i.e., admitting the presence of a Strongly-Connected Component (SCC), an IN-component (together with some tendrils attached to it) and an OUT-component. Interestingly, the evolution of the BUN structural organisation experiences fluctuations that seem to be correlated with the presence of “bubbles”, i.e., periods of price surge and decline observed throughout its entire history. Our results, thus, further confirm the interplay between structural quantities and price movements reported by previous analyses.

Author Biography

Nicolò Vallarano, Department of Informatics and UZH Blockchain Center, University of Zurich, Switzerland

Nicolò Vallarano's fields of research range between the statistical mechanics of networks and distributed ledger technologies. He's a research associate at UZH Blockchain and Decentralized Ledger Techonology (BDLT) group modelling consensus protocols other than the classic Bitcoin Proof-of-Work. As part of his research activity he collaborates with the Blockchain Observatory in the study and classification of cryptocurrencies' economic state.

References

Aldecoa, R., Marín, I. “Exploring the Limits of Community Detection Strategies in Complex Networks.” Scientific Reports 3.1 2216 (2013) https://doi.org/10.1038/srep02216.

Aldecoa, R., Marín, I. “Surprise Maximization Reveals the Community Structure of Complex Networks.” Scientific Reports 3.1 1060 (2013) https://doi.org/10.1038/srep01060.

Androulaki, E., Karame, G. O., Roeschlin, M., Scherer, T., Capkun, S. “Evaluating User Privacy in Bitcoin.” In A. Sadeghi (Ed.), International Conference on Financial Cryptography and Data Security 34–51 (2013) https://doi.org/10.1007/978-3-642-39884-1_4.

Antonopoulos, A. M. Mastering Bitcoin: Programming the Open Blockchain. Sebastopol: O’Reilly Media, Inc. (2017).

Barabási, A.-L. “Scale-Free Networks: A Decade and Beyond.” Science 325.5939 412–413 (2009) https: //doi.org/10.1126/science.1173299.

Bardoscia, M., Battiston, S., Caccioli, F., Caldarelli, G. “DebtRank: A Microscopic Foundation for Shock Propagation.” PloS one 10.6 e0130406 (2015) https://doi.org/10.1371/journal.pone.0130406.

Bovet, A., et al. “The Evolving Liaisons Between the Transaction Networks of Bitcoin and Its Price Dynamics.” In Proceedings of Blockchain Kaigi 2022 (BCK22) 011002 (2023) https://doi.org/10.7566/ JPSCP.40.011002.

Crucitti, P., Latora, V., Porta, S. “Centrality Measures in Spatial Networks of Urban Streets.” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 73.3 036125 (2006) https://doi.org/10.1103/ PhysRevE.73.036125.

de Jeude, J. v. L., Caldarelli, G., Squartini, T. “Detecting Core-Periphery Structures by Surprise.” Europhysics Letters 125.6 68001 (2019) https://doi.org/10.1209/0295-5075/125/68001.

De Masi, G., Iori, G., Caldarelli, G. “Fitness Model for the Italian Interbank Money Market.” Physical Review E 74.6 066112 (2006) https://doi.org/10.1371/journal.pone.0130406.

Decker, C., Wattenhofer, R. “Bitcoin Transaction Malleability and MtGox.” In M. Kutyłowski, J. Vaidya (Eds.), Computer Security - ESORICS 2014 Cham: Springer International Publishing 313–326 (2014) https: //doi.org/10.1007/978-3-319-11212-1_18.

Different results have been reported in Maesa et al. (2019), where the authors observe the dominance of the SCC over the other components across the years 2009-2015. Such a result may be explained by the fact that i) the heuristic clustering is applied only until 2015; ii) only the multi-input one is employed; iii) transactions are aggregated every 55 days.42

Dixon, P. M., Weiner, J., Mitchell-Olds, T., Woodley, R. “Bootstrapping the Gini Coefficient of Inequality.” Ecology 68.5 1548–1551 (1987) https://doi.org/10.2307/1939238.

Fischer, J. A., Palechor, A., Dell’Aglio, D., Bernstein, A., Tessone, C. J. “The Complex Community Structure of the Bitcoin Address Correspondence Network.” Frontiers in Physics 9 681798 (2021) https: //doi.org/10.3389/fphy.2021.681798.

Freeman, L. C. “Centrality in Social Networks Conceptual Clarification.” Social Networks 1.3 215–239 (1978) https://doi.org/10.1016/0378-8733(78)90021-7.

Garlaschelli, D., Loffredo, M. I. “Maximum Likelihood: Extracting Unbiased Information from Complex Networks.” Physical Review E 78.1 015101 (2008) https://doi.org/10.1103/PhysRevE.78.015101.

Glaser, F. “Pervasive Decentralisation of Digital Infrastructures: A Framework for Blockchain Enabled System and Use Case Analysis.” In Proceedings of the Hawaii International Conference on System Sciences 2017 (HICSS-50) 1543–1552 (2017) https://doi.org/10.5445/IR/1000073702.

Halaburda, H., Sarvary, M. Beyond Bitcoin: The Economics of Digital Currencies. New York: Palgrave Macmillan (2016).

Harrigan, M., Fretter, C. “The Unreasonable Effectiveness of Address Clustering.” In Ubiquitous In- telligence & Computing, Advanced and Trusted Computing, Scalable Computing and Communications, Cloud and Big Data Computing, Internet of People, and Smart World Congress (UIC/ATC/ScalCom/CB- DCom/IoP/SmartWorld), 2016 Intl IEEE Conferences IEEE 368–373 (2016) https://doi.org/10.1109/ UIC-ATC-ScalCom-CBDCom-IoP-SmartWorld.2016.0071.

Javarone, M. A., Wright, C. S. “From Bitcoin to Bitcoin Cash: A Network Analysis.” In Proceedings of the 1st Workshop on Cryptocurrencies and Blockchains for Distributed Systems 77–81 (2018) https: //doi.org/10.1145/3211933.3211947.

Khakzad, N., Khan, F., Amyotte, P. “Dynamic Risk Analysis Using Bow-Tie Approach.” Reliability Engineering & System Safety 104 36–44 (2012) https://doi.org/10.1016/j.ress.2012.04.003.

Kondor, D., Pósfai, M., Csabai, I., Vattay, G. “Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network.” PloS one 9.2 e86197 (2014) https://doi.org/10.1371/journal.pone.0086197.

Lin, J.-H., Marchese, E., Tessone, C. J., Squartini, T. “The Weighted Bitcoin Lightning Network.” Chaos, Solitons & Fractals 164 112620 (2022) https://doi.org/10.1016/j.chaos.2022.112620.

Lin, J.-H., Primicerio, K., Squartini, T., Decker, C., Tessone, C. J. “Lightning Network: A Second Path Towards Centralisation of the Bitcoin Economy.” New Journal of Physics 22.8 083022 (2020) https://doi. org/10.1088/1367-2630/aba062.

Maesa, D. D. F., Marino, A., Ricci, L. “The Bow Tie Structure of the Bitcoin Users Graph.” Applied Network Science 4.1 1–22 (2019) https://doi.org/10.1007/s41109-019-0163-y.

Marchese, E., Caldarelli, G., Squartini, T. “Detecting Mesoscale Structures by Surprise.” Communications Physics 5.1 132 (2022) https://doi.org/10.1038/s42005-022-00890-7.

Morgan, J. “The Anatomy of Income Distribution.” The Review of Economics and Statistics 44.3 270–283 (1962) https://doi.org/10.2307/1926398.

Möser, M., Narayanan, A. “Resurrecting Address Clustering in Bitcoin.” In I. Eyal, J. Garay (Eds.), International Conference on Financial Cryptography and Data Security 386–403 (2022) https://doi.org/ 10.1007/978-3-031-18283-9_19.

Nakamoto, S. “Bitcoin: A Peer-to-Peer Electronic Cash System.” (2008) (accessed 24 October 2024) https://bitcoin.org/bitcoin.pdf.

Newman, M. E. “Mixing Patterns in Networks.” Physical Review E 67.2 026126 (2003) https://doi. org/10.1103/PhysRevE.67.026126.

Newman, M. Networks. Oxford: Oxford University Press (2018).

Nicolini, C., Bifone, A. “Modular Structure of Brain Functional Networks: Breaking the Resolution Limit by Surprise.” Scientific Reports 6.1 19250 (2016) https://doi.org/10.1038/srep19250.

Noldus, R., Van Mieghem, P. “Assortativity in Complex Networks.” Journal of Complex Networks 3.4 507–542 (2015) https://doi.org/10.1093/comnet/cnv005.

Rodrigues, F. A. “Network Centrality: An Introduction.” In E. Macau (Ed.), A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems Springer 177–196 (2019) https://doi.org/10. 1007/978-3-319-78512-7_10.

Rombach, M. P., Porter, M. A., Fowler, J. H., Mucha, P. J. “Core-Periphery Structure in Networks.” SIAM Journal on Applied Mathematics 74.1 167–190 (2014) https://doi.org/10.1137/120881683.

Ron, D., Shamir, A. “Quantitative Analysis of the Full Bitcoin Transaction Graph.” In International Conference on Financial Cryptography and Data Security Springer 6–24 (2013) https://doi.org/10. 1007/978-3-642-39884-1_2.

Schweitzer, F., Fagiolo, G., Sornette, D., Vega-Redondo, F., White, D. R. “Economic Networks: What Do We Know and What Do We Need to Know?” Advances in Complex Systems 12.04n05 407–422 (2009) https://doi.org/10.1142/S0219525909002337.

Squartini, T., Garlaschelli, D. “Stationarity, Non-Stationarity and Early Warning Signals in Economic Networks.” Journal of Complex Networks 3.1 1–21 (2015) https://doi.org/10.1093/comnet/cnu012.

Squartini, T., van Lelyveld, I., Garlaschelli, D. “Early-Warning Signals of Topological Collapse in Interbank Networks.” Scientific Reports 3 3357 (2013) https://doi.org/10.1038/srep03357.

Tasca, P., Hayes, A., Liu, S. “The Evolution of the Bitcoin Economy: Extracting and Analyzing the Network of Payment Relationships.” Journal of Risk Finance 19.2 94–126 (2018) https://doi.org/10. 1108/JRF-03-2017-0059.

Van Lidth De Jeude, J., Di Clemente, R., Caldarelli, G., Saracco, F., Squartini, T. “Reconstructing Mesoscale Network Structures.” Complexity 2019.1 5120581 (2019) https://doi.org/10.1155/2019/5120581.

Wheatley, S., Sornette, D., Huber, T., Reppen, M., Gantner, R. N. “Are Bitcoin Bubbles Predictable? Combining a Generalized Metcalfe’s Law and the Log-Periodic Power Law Singularity Model.” Royal Society Open Science 6.6 180538 (2019) https://doi.org/10.1098/rsos.180538.

Downloads

Additional Files

Published

2025-01-21

How to Cite

Vallarano, N., Squartini, T., & Tessone, C. J. (2025). Exploring the Mesoscopic Structure of Bitcoin During its First Decade of Life. Ledger, 9. https://doi.org/10.5195/ledger.2024.335

Issue

Vol. 9 (2024)

Section

ChainScience Invitational Articles

License

Copyright (c) 2025 Nicolò Vallarano, Tiziano Squartini, Claudio J. Tessone

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

  1. The Author retains copyright in the Work, where the term “Work” shall include all digital objects that may result in subsequent electronic publication or distribution.
  2. Upon acceptance of the Work, the author shall grant to the Publisher the right of first publication of the Work.
  3. The Author shall grant to the Publisher and its agents the nonexclusive perpetual right and license to publish, archive, and make accessible the Work in whole or in part in all forms of media now or hereafter known under a Creative Commons Attribution 4.0 International License or its equivalent, which, for the avoidance of doubt, allows others to copy, distribute, and transmit the Work under the following conditions:
    1. Attribution—other users must attribute the Work in the manner specified by the author as indicated on the journal Web site;
    with the understanding that the above condition can be waived with permission from the Author and that where the Work or any of its elements is in the public domain under applicable law, that status is in no way affected by the license.
  4. The Author is able to enter into separate, additional contractual arrangements for the nonexclusive distribution of the journal's published version of the Work (e.g., post it to an institutional repository or publish it in a book), as long as there is provided in the document an acknowledgement of its initial publication in this journal.
  5. Authors are permitted and encouraged to post online a prepublication manuscript (but not the Publisher’s final formatted PDF version of the Work) in institutional repositories or on their Websites prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work. Any such posting made before acceptance and publication of the Work shall be updated upon publication to include a reference to the Publisher-assigned DOI (Digital Object Identifier) and a link to the online abstract for the final published Work in the Journal.
  6. Upon Publisher’s request, the Author agrees to furnish promptly to Publisher, at the Author’s own expense, written evidence of the permissions, licenses, and consents for use of third-party material included within the Work, except as determined by Publisher to be covered by the principles of Fair Use.
  7. The Author represents and warrants that:
    1. the Work is the Author’s original work;
    2. the Author has not transferred, and will not transfer, exclusive rights in the Work to any third party;
    3. the Work is not pending review or under consideration by another publisher;
    4. the Work has not previously been published;
    5. the Work contains no misrepresentation or infringement of the Work or property of other authors or third parties; and
    6. the Work contains no libel, invasion of privacy, or other unlawful matter.
  8. The Author agrees to indemnify and hold Publisher harmless from Author’s breach of the representations and warranties contained in Paragraph 6 above, as well as any claim or proceeding relating to Publisher’s use and publication of any content contained in the Work, including third-party content.
  9. The Author agrees to digitally sign the Publisher’s final formatted PDF version of the Work.

Revised 7/16/2018. Revision Description: Removed outdated link.