In this paper, we use the methods of networks science to analyse the transaction networks of tokens running on the Ethereum blockchain. We start with a deep dive on four of them: Ampleforth (AMP), Basic Attention Token (BAT), Dai (DAI) and Uniswap (UNI). We study two types of blockchain addresses, smart contracts (SC), which run code, and externally owned accounts (EOA), run by human users, or off-chain code, with the corresponding private keys. We use preferential attachment and network dismantling strategies to evaluate their importance for the network structure. Subsequently, we expand our view to all ERC-20 tokens issued on the Ethereum network. We first study multilayered networks composed of Ether (ETH) and individual tokens using a dismantling approach to assess how the deconstruction starting from one network affects the other. Finally, we analyse the Ether network and Ethereum-based token networks to find similarities between sets of high-degree nodes. For this purpose, we use both the traditional Jaccard Index and a new metric that we introduce, the Ordered Jaccard Index (OJI), which considers the order of the elements in the two sets that are compared. Our findings suggest that smart contracts and exchange-related addresses play a structural role in transaction networks both in DeFi and Ethereum. The presence in the network of nodes associated to addresses of smart contracts and exchanges is positively correlated with the success of the token network measured in terms of network size and market capitalisation. These nodes play a fundamental role in the centralisation of the supposedly decentralised finance (DeFi) ecosystem: without them, their networks would quickly collapse.

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The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets

Bitcoin (BTC) and Ethereum (ETH), pioneering public blockchains implementations, are two fundamental levers to register and transfer digital value. This article studies the structure of their daily price volatility time series following a multifaceted approach: first, it examines the existence of chaoticity and fractality in the time series. Obtained results confirm that the BTC and ETH price volatility series present signs of chaoticity, persistence of a long-term correlation and multifractality. Second, it analyses the corresponding visibility graphs associated with these time series using complex network theory. The undirected and connected complex networks, spawned by their natural visibility graphs (VGs) and horizontal visibility graphs (HVGs), present a hierarchical structure. These networks, especially the HVGs, confirm the fractality of the originating time series. The study of HVGs also confirms a lack of uncorrelated randomness in the originating BTC and ETH price series. This paper validates the value of visibility graphs as useful proxies to better understand complex time series, in this case, related to public blockchain implementations. • Bitcoin and Ethereum are fundamental levers to register and transfer digital value. • Multifaceted analysis of Bitcoin and Ethereum prices: time series & visibility graphs. • Bitcoin and Ethereum price series display chaoticity and multifractality. • Obtained visibility graphs display a hierarchy and hint fractality in original series. • Visibility graphs are useful proxies to better understand complex time series. 

The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series

A framework for maintaining sustainable energy use in Bitcoin mining through switching efficient mining hardware

The Grains and Oilseeds Index (GOI) and its sub-indices of wheat, maize, soyabeans, rice, and barley are daily price indexes reflect the price changes of the global spot markets of staple agro-food crops. In this paper, we carry out a visibility graph (VG) analysis of the GOI and its five sub-indices. Maximum likelihood estimation shows that the degree distributions of the VGs display power-law tails, except for rice. The average clustering coefficients of the six VGs are quite large (>0.5) and exhibit a nice power-law relation with respect to the average degrees of the VGs. For each VG, the clustering coefficients of nodes are inversely proportional to their degrees for large degrees and are correlated to their degrees as a power law for small degrees. All the six VGs exhibit small-world characteristics to some extent. The degree-degree correlation coefficients shows that the VGs for maize and soyabeans indices exhibit weak assortative mixing patterns, while the other four VGs are weakly disassortative. The average nearest neighbor degree functions have similar patterns, and each function shows a more complex mixing pattern which decreases for small degrees, increases for mediate degrees, and decreases again for large degrees.

Visibility graph analysis of the grains and oilseeds indices

In this article, we model the two most market-capitalised public, open and permissionless blockchain implementations, Bitcoin (BTC) and Ethereum (ETH), as a System of Systems (SoS) of public blockchains. We study the concepts of blockchain, BTC, ETH, complex networks, SoS Engineering and intentional risk. We analyse BTC and ETH from an open SoS perspective through the main properties that seminal System of Systems Engineering (SoSE) references propose. This article demonstrates that these public blockchain implementations create networks that grow in complexity and connect with each other. We propose a methodology based on a complexity management lever such as SoSE to better understand public blockchains such as BTC and ETH and manage their evolution. Our ultimate objective is to improve the resilience of public blockchains against intentional risk: a key requirement for their mass adoption. We conclude with specific measures, based on this novel systems engineering approach, to effectively improve the resilience against intentional risk of the open SoS of public blockchains, composed of a non-inflationary money system, “sound money”, such as BTC, and of a world financial computer system, “a financial conduit”, such as ETH. The goal of this paper is to formulate a SoS that transfers digital value and aspires to position itself as a distributed alternative to the fiat currency-based financial system.

https://www.mdpi.com/2079-9292/11/2/241/pdf?version=1642065450

Javier Taboada

Papers

Modeling Bitcoin plus Ethereum as an Open System of Systems of Public Blockchains to Improve Their Resilience against Intentional Risk

The chaotic, self-similar and hierarchical patterns in Bitcoin and Ethereum price series