Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens between participants. The availability of the complete historical bookkeeping opens up an unprecedented possibility: that of understanding the evolution of a cryptocurrency's network structure while gaining useful insights into the relationships between users' behavior and cryptocurrency pricing in exchange markets. In this article we review some recent results concerning the structural properties of the Bitcoin Transaction Networks, a generic name referring to a set of three different constructs: the Bitcoin Address Network, the Bitcoin User Network, and the Bitcoin Lightning Network. The picture that emerges is of a system growing over time, which becomes increasingly sparse and whose mesoscopic structural organization is characterized by the presence of an increasingly significant core-periphery structure. Such a peculiar topology is accompanied by a highly uneven distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralized system at different levels.

Hierarchical organization is an important, prevalent characteristic of complex systems; to understand their organization, the study of the underlying (generally complex) networks that describe the interactions between their constituents plays a central role. Numerous previous works have shown that many real-world networks in social, biologic, and technical systems present hierarchical organization, often in the form of a hierarchy of community structures. Many artificial benchmark graphs have been proposed to test different community detection methods, but no benchmark has been developed to thoroughly test the detection of hierarchical community structures. In this study, we fill this vacancy by extending the Lancichinetti-Fortunato-Radicchi (LFR) ensemble of benchmark graphs, adopting the rule of constructing hierarchical networks proposed by Ravasz and Barabási. We employ this benchmark to test three of the most popular community detection algorithms and quantify their accuracy using the traditional mutual information and the recently introduced hierarchical mutual information. The results indicate that the Ravasz-Barabási-Lancichinetti-Fortunato-Radicchi (RB-LFR) benchmark generates a complex hierarchical structure constituting a challenging benchmark for the considered community detection methods.

The core of many cryptocurrencies is the decentralised validation network operating on proof-of-work technology. In these systems, validation is done by so-called miners who can digitally sign blocks once they solve a computationally-hard problem. Conventional wisdom generally considers this protocol as secure and stable as miners are incentivised to follow the behaviour of the majority. However, whether some strategic mining behaviours occur in practice is still a major concern. In this paper we target this question by focusing on a security threat: a selfish mining attack in which malicious miners deviate from protocol by not immediately revealing their newly mined blocks. We propose a statistical test to analyse each miner’s behaviour in five popular cryptocurrencies: Bitcoin, Litecoin, Monacoin, Ethereum and Bitcoin Cash. Our method is based on the realisation that selfish mining behaviour will cause identifiable anomalies in the statistics of miner’s successive blocks discovery. Secondly, we apply heuristics-based address clustering to improve the detectability of this kind of behaviour. We find a marked presence of abnormal miners in Monacoin and Bitcoin Cash, and, to a lesser extent, in Ethereum. Finally, we extend our method to detect coordinated selfish mining attacks, finding mining cartels in Monacoin where miners might secretly share information about newly mined blocks in advance. Our analysis contributes to the research on security in cryptocurrency systems by providing the first empirical evidence that the aforementioned strategic mining behaviours do take place in practice.

We present a novel analysis of a competitive dynamic present on Ethereum known as "waiting games", where validators can use their distinct monopoly position in their assigned slots to delay block proposals in order to optimize returns through Maximal Extractable Value (MEV) payments, a type of incentive outside the Proof-of-Stake incentive scheme. However, this strategy risks block exclusion due to missed slots or potential orphaning. Our analysis reveals evidence that, although there are substantial incentives to undertaking the risks, validators are not capitalizing on waiting games, leaving potential profits unrealized. Moreover, we present an agent-based model to test the eventual consensus disruption caused by waiting games under different settings, arguing that such disruption only occurs with significant delay strategies. Ultimately, this research provides in-depth insights into Ethereum's waiting games, illuminating the trade-offs and potential profit opportunities for validators in this evolving blockchain landscape.

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust, and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the hierarchical mutual information, which is a generalization of the traditional mutual information and makes it possible to compare hierarchical partitions and hierarchical community structures. The normalized version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information, namely the comparison of different community detection methods and the study of the consistency, robustness, and temporal evolution of the hierarchical modular structure of networks.