Bitcoin Transaction Networks: An Overview of Recent Results

Vallarano, Nicolò; Tessone, Claudio J.; Squartini, Tiziano

doi:10.3389/fphy.2020.00286

Cited by 33 publications

(29 citation statements)

References 32 publications

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“…The observation that the term appears on both sides of the equation corresponding to the i -th constraint suggests an iterative recipe to solve such a system, i.e. originally proposed in 22 and further refined in 23 . The identification , allows the probability coefficients defining the UBCM to be numerically determined.…”

Section: Applicationsmentioning

confidence: 99%

“…Problems like these are usually affected by the issues of accuracy , speed and scalability : the present paper aims at addressing them at once, by comparing the performance of three algorithms, i.e. Newton’s method, a quasi-Newton method and a recently-proposed fixed-point recipe 22 , 23 , to solve a variety of ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion.…”

Section: Introductionmentioning

confidence: 99%

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Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

Vallarano

Marchese

Trapani

et al. 2021

Sci Rep

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Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant patterns in graphs, counting networked configurations with given properties. From a technical point of view, the ERGMs workflow is defined by two subsequent optimization steps: the first one concerns the maximization of Shannon entropy and leads to identify the functional form of the ensemble probability distribution that is maximally non-committal with respect to the missing information; the second one concerns the maximization of the likelihood function induced by this probability distribution and leads to its numerical determination. This second step translates into the resolution of a system of O(N) non-linear, coupled equations (with N being the total number of nodes of the network under analysis), a problem that is affected by three main issues, i.e. accuracy, speed and scalability. The present paper aims at addressing these problems by comparing the performance of three algorithms (i.e. Newton’s method, a quasi-Newton method and a recently-proposed fixed-point recipe) in solving several ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion. While Newton’s method performs best for relatively little networks, the fixed-point recipe is to be preferred when large configurations are considered, as it ensures convergence to the solution within seconds for networks with hundreds of thousands of nodes (e.g. the Internet, Bitcoin). We attach to the paper a Python code implementing the three aforementioned algorithms on all the ERGMs considered in the present work.

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Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

Vallarano

Marchese

Trapani

et al. 2021

Sci Rep

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“…5, in an economy where the "consumption functions" incorporated P i (τ ) are homogeneous, M i would be the only factor to generate diversity in MicroVelocity. The systems we analyze have high wealth concentration, which is a tendency that is common to cryptocurrencies [21,22,23,24]. This is likely due to large pseudo-banking companies that arise naturally in the environment, acting as exchange markets for fiat currencies or as vaults where crypto users securely store their tokens [25].…”

Section: Resultsmentioning

confidence: 99%

MicroVelocity: rethinking the Velocity of Money for digital currencies

Campajola¹,

D’Errico²,

Tessone³

2022

Preprint

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We propose a novel framework to analyse the velocity of money in terms of the contribution (MicroVelocity) of each individual agent, and to uncover the distributional determinants of aggregate velocity. Leveraging on complete publicly available transactions data stored in blockchains from four cryptocurrencies, we empirically find that MicroVelocity i) is very heterogeneously distributed and ii) strongly correlates with agents' wealth. We further document the emergence of high-velocity intermediaries, thereby challenging the idea that these systems are fully decentralised. Further, our framework and results provide policy insights for the development and analysis of digital currencies.

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“…Public blockchains are current examples of complex systems which are increasingly researched through complex network approaches Vallarano et al [11]. By analysing a complete and unique dataset encompassing the first 5 years of Ethereum platform, i.e., 856,207,725 transactions and 87,780,546 addresses, we show that the native cryptocurrency of the Ethereum platform, Ether, and the most active tokens on it show a form of preferential attachment, with signs of superlinear PA.…”

Section: Introductionmentioning

confidence: 80%

“…The additional research boundary is the considerable amount of data that blockchain implementations produce when they are massively adopted. Extant research by [8][9][10][11] shows that market value growth has accelerated in parallel to the number of users and transactions. While in some cases, like in Bitcoin, the rate of data production is currently bounded by the limits imposed by design choices (block size, inter-block time), and in other systems, transaction data increase massively throughout time (like in Ethereum).…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous Preferential Attachment in Key Ethereum-Based Cryptoassets

et al. 2021

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In this study, we analyse the aggregated transaction networks of Ether (the native cryptocurrency in Ethereum) and the three most market-capitalised ERC-20 tokens in this platform at the time of writing: Binance, USDT, and Chainlink. We analyse a comprehensive dataset from 2015 to 2020 (encompassing 87,780,546 nodes and 856,207,725 transactions) to understand the mechanism that drives their growth. In a seminal analysis, Kondor et al. (PLoS ONE, 2014, 9: e86197) showed that during its first year, the aggregated Bitcoin transaction network grew following linear preferential attachment. For the Ethereum-based cryptoassets, we find that they present in general super-linear preferential attachment, i.e., the probability for a node to receive a new incoming link is proportional to kα, where k is the node’s degree. Specifically, we find an exponent α = 1.2 for Binance and Chainlink, for Ether α = 1.1, and for USDT α = 1.05. These results reveal that few nodes become hubs rapidly. We then analyse wealth and degree correlation between tokens since many nodes are active simultaneously in different networks. We conclude that, similarly to what happens in Bitcoin, “the rich indeed get richer” in Ethereum and related tokens as well, with wealth much more concentrated than in-degree and out-degree.

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Bitcoin Transaction Networks: An Overview of Recent Results

Cited by 33 publications

References 32 publications

Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

MicroVelocity: rethinking the Velocity of Money for digital currencies

Heterogeneous Preferential Attachment in Key Ethereum-Based Cryptoassets

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