The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.
This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) using the Complexity--Entropy Causality Plane (CECP) and directed horizontal visibility graphs (directed HVG) to uncover complex temporal patterns and time-directed structures in the return series. While conventional stylized facts show striking convergence across all assets, structural diagnostics reveal a compelling paradox: cryptocurrencies appear more locally random than the equity benchmark during ordinary periods, yet exhibit significantly stronger directional time-irreversibility around high-visibility return events. The absolute-return results show that large cryptocurrency fluctuations tend to begin abruptly and remain elevated afterward. Separate analyses of positive returns and negative-return magnitudes show that this pattern is shared across cryptocurrencies on the upside but varies across assets on the downside. We conclude that statistical maturity is only skin-deep; the underlying dynamical processes of mature cryptocurrencies remain fundamentally distinct from traditional benchmarks.
Klaus M. Frahm, Leonardo Ermann, Dima L. Shepelyansky
According to the recent Wealth Thermalization Hypothesis (WTH) the wealth inequality in the world is described by the Rayleigh-Jeans (RJ) thermal distribution of interacting agents in a society with social stratification. In this concept, the wealth layers of society are associated with energy levels from a nonlinear dynamical system conserving two integrals of motion being total energy and probability norm. This leads to RJ condensation and the formation of a huge poverty phase of low wealth and a tiny oligarchic phase that captures a main part of total society wealth. This RJ phenomenon has similarities with self cleaning in multimode optical fibers and constraint driven condensation in various physical systems. We analyze real Lorenz and Pareto curves for wealth of households in countries and the world, Gross Domestic Product of countries, market capitalization of companies at stock exchange of Hong Kong, Shanghai, London, bitcoin transactions, world trade between countries and show that the WTH theory gives a good description of these curves. On the basis of this comparison we argue that the RJ thermal distribution provides a universal description of wealth inequality in the world.
Deep Nath, Paolo Tasca, Nikhil Vadgama, Marco Alberto Javarone
Quantifying structural stress in transaction networks requires metrics that capture structural organization beyond transaction volume alone. In this work, we introduce the Inefficiency Metric, a deterministic indicator designed to characterize the routing structure of capital flows in decentralized systems. Using Principal Component Analysis and Pearson correlation matrices computed from a six-year Hedera transaction dataset, we identify two dominant and largely independent structural dimensions: the effective diameter, related to the spatial extension of transaction propagation, and the closeness centrality, associated with the efficiency of network-level flow processing. The proposed metric reveals significant topological fluctuations associated with major macroeconomic and ecosystem-level events. Increased inefficiency is observed during periods marked by intermediary fragmentation or rapid smart-contract expansion, whereas lower inefficiency corresponds to phases of network compaction during market stress or institutional concentration. Comparison with a seven-dimensional Isolation Forest approach shows that the metric effectively captures severe multidimensional anomalies while preserving a clear structural interpretation. Overall, these results provide a physics-inspired framework for relating the large-scale organization of decentralized transaction networks to observable economic dynamics.
Jeong-Hyuck Park, Chanhee Park, Claudio J. Tessone, Yu Zhang
Digitalisation transforms money from distinguishable physical objects into fungible informational units. A recent theoretical framework predicts that such indistinguishable wealth obeys bosonic occupancy statistics, leading to geometric ownership distributions and enhanced inequality. Using Bitcoin blockchain data, we test this prediction on 63 UTXO denominations across 72 monthly snapshots (2018--2023). A one-parameter geometric model describes the ownership distributions, reproducing both mean holdings and their temporal evolution; Jensen--Shannon divergence values lie below $0.08$ in $99.74\%$ of cases. The inferred inverse-temperature parameter satisfies the analytic mean--temperature relation to better than $0.1\%$ in every sample -- a self-consistency test that two-parameter alternatives cannot pass -- and remains within a narrow band across eight orders of magnitude in denomination and over six years. Bitcoin UTXO ownership statistics are therefore consistent with bosonic occupancy laws, suggesting that the informational nature of electronic money may act as a structural driver of inequality in digital economies.
Do Ethereum's Layer-2 (L2) rollups actually decongest the Layer-1 (L1) mainnet once protocol upgrades and demand are held constant? Using a 1245-day daily panel from August 5, 2021 to December 31, 2024 that spans the London, Merge, and Dencun upgrades, we link Ethereum fee and congestion metrics to L2 user activity, macro-demand proxies, and targeted event indicators. We estimate a regime-aware error-correction model that treats posting-clean L2 user share as a continuous treatment. Over the pre-Dencun (London+Merge) window, a 10 percentage point increase in L2 adoption lowers median base fees by about 13% -- roughly 5 Gwei at pre-Dencun levels -- and deviations from the long-run relation decay with an 11-day half-life. Block utilization and a scarcity index show similar congestion relief. After Dencun, L2 adoption is already high and treatment support narrows, so blob-era estimates are statistically imprecise and we treat them as exploratory. The pre-Dencun window therefore delivers the first cross-regime causal estimate of how aggregate L2 adoption decongests Ethereum, together with a reusable template for monitoring rollup-centric scaling strategies.
Duniter-based cryptocurrencies, which are providing a kind of universal basic income, are using a system called "Web of Trust" based on a social network whose evolution is subject to graph theoretical rules, time constraints and a licence in order to avoid large Sybil attacks. We investigate in this article the largest size of a Sybil attack that a simplified version of the graph theoretical rules of a Web of Trust can undergo depending on the number of attackers and on the parameters of the system. We show that even if in theory, without considering social and time constraints, this system cannot in general prevent huge attacks, in the real-world case of a Duniter-based cryptocurrency (with thousands of users), the system can prevent attacks of large size with only graph theoretical rules.
Technological developments and the impact of artificial intelligence (AI) are omnipresent themes and concerns of the present day. Much has been written on these topics but applications of quantitative models to understand the techno-social landscape have been much more limited. We propose a mathematical model that can help understand in a unified manner the patterns underlying technological development and also identify the different regimes in which the technological landscape evolves. First, we develop a model of innovation diffusion between different technologies, the growth of each reinforcing the development of the others. The model has a variable that quantifies the level of development (or innovation, discovery) potential for a given technology. The potential, or market capacity, increases via diffusion from related technologies, reflecting the fact that a technology does not develop in isolation. Hence, the growth of each technology is influenced by how developed its neighboring (related) technologies are. This allows us to reproduce long-term trends seen in computing technology and large language models (LLMs). We then present a three-dimensional system of supply, demand, and investment which shows oscillations (business cycles) emerging if investment is too high into a given technology, product, or market. We finally combine the two models through a common variable and show that if investment or diffusion is too high in the network context, chaotic boom-bust cycles can emerge. These quantitative considerations allow us to reproduce the boom-bust patterns seen in non-fungible token (NFT) transaction data and also have deep implications for the development of AI which we highlight, such as the arrival of a new AI winter.
Abstract This study provides essential insights into how diffusion processes unfold in complex networks, with a focus on cryptocurrency blockchains and infrastructure networks. The structural properties of these networks, such as hub-dominated, heavy-tailed topology, network motifs, and node centrality, significantly influence diffusion speed and reach. Using epidemic diffusion models, specifically the Kertesz threshold model and the Susceptible-Infected (SI) model, we analyze key factors affecting diffusion dynamics. To assess the uncertainty in the fraction of infected nodes over time, we employ bootstrap confidence intervals, while Bayesian credible intervals are constructed to quantify parameter uncertainties in the SI models. Our findings reveal substantial variations across different network types, including Erdős-Rényi networks, Geometric Random Graphs, and Delaunay Triangulation networks, emphasizing the role of network architecture in failure propagation. We identify that network motifs are crucial in diffusion. We highlight that hub-dominated networks, which dominate blockchain ecosystems, provide resilience against random failures but remain vulnerable to targeted attacks, posing significant risks to network stability. Furthermore, centrality measures such as degree, betweenness, and clustering coefficient strongly influence the transmissibility of diffusion in both blockchain and critical infrastructure networks.
An Pham Ngoc Nguyen, Marija Bezbradica, Martin Crane
As global financial markets become increasingly interconnected, financial contagion has developed into a major influencer of asset price dynamics. Motivated by this context, our study explores financial contagion both within and between asset communities. We contribute to the literature by examining the contagion phenomenon at the community level rather than among individual assets. Our experiments rely on high-frequency data comprising cryptocurrencies, stocks and US ETFs over the 4-year period from April 2019 to May 2023. Using the Louvain community detection algorithm, Vector Autoregression contagion detection model and Tracy-Widom random matrix theory for noise removal from financial assets, we present three main findings. Firstly, while the magnitude of contagion remains relatively stable over time, contagion density (the percentage of asset pairs exhibiting contagion within a financial system) increases. This suggests that market uncertainty is better characterized by the transmission of shocks more broadly than by the strength of any single spillover. Secondly, there is no significant difference between intra- and inter-community contagion, indicating that contagion is a system-wide phenomenon rather than being confined to specific asset groups. Lastly, certain communities themselves, especially those dominated by Information Technology assets, tend to act as major contagion transmitters in the financial network over the examined period, spreading shocks with high densities to many other communities. Our findings suggest that traditional risk management strategies such as portfolio diversification through investing in low-correlated assets or different types of investment vehicle might be insufficient due to widespread contagion.
Asset exchange models (AEMs) provide a physics-inspired framework for studying wealth formation. These models capture wealth distribution dynamics via pairwise money exchanges, yielding steady-state distributions from exponential to heavy-tailed power laws. However, empirical validation remains limited due to scarce real-world transaction data. Here, we bridge this gap by analyzing spectral properties of Markov transition matrices from both AEMs and Ethereum blockchain data, enabling quantitative comparison of model and empirical exchange dynamics. We assess thermodynamic equilibrium in exchange processes - specifically, detailed balance - and derive steady-state wealth distributions from transition matrices. We find that equilibrium systems' spectra contain only real eigenvalues and link Ethereum price changes to spectral shifts. We also investigate external factors (e.g., taxes), showing that advantages for richer individuals make wealth evolution path-dependent on initial distributions. Our work establishes a quantitative framework for validating AEMs with real data, advancing economic modeling and understanding of wealth formation.
Stergios Intzes, Georgios D. Papadopoulos, Lykourgos Magafas
Our analysis focuses on the stock cryptocurrency market, by studying a group of nineteen cryptocurrencies where their capitalisation is about 99% of the total market. Specifically, it is examined this group of cryptocurrencies for the period from 2017 up to 2024, taking into account the effect of COVID-19 pandemic. As far as we know, this is the first time that this kind of study has been published, where it takes place by creating various networks based on stock cryptocurrency correlation, in order to be possible to visualise and access these relationships using methods from Complex Networks. The evaluation results show that, there are three different communities within the crypto market and although COVID-19 pandemic and ongoing geopolitical changes, there is a notable trend towards an increase in the number of cryptocurrencies. Additionally, it is applied discriminant analysis to identify the differences among various cryptocurrencies based on their features.
Kundan Mukhia, SR Luwang, Md. Nurujjaman, Tanujit Chakraborty · 6 authors
Scaling laws offer a powerful lens to understand complex transactional behaviors in decentralized systems. This study reveals distinctive statistical signatures in the transactional dynamics of ERC20 tokens on the Ethereum blockchain by examining over 44 million token transfers between July 2017 and March 2018 (9-month period). Transactions are categorized into four types: EOA--EOA, EOA--SC, SC-EOA, and SC-SC based on whether the interacting addresses are Externally Owned Accounts (EOAs) or Smart Contracts (SCs), and analyzed across three equal periods (each of 3 months). To identify universal statistical patterns, we investigate the presence of two canonical scaling laws: power law distributions and temporal Taylor's law (TL). EOA-driven transactions exhibit consistent statistical behavior, including a near-linear relationship between trade volume and unique partners with stable power law exponents ($γ\approx 2.3$), and adherence to TL with scaling coefficients ($β\approx 2.3$). In contrast, interactions involving SCs, especially SC-SC, exhibit sublinear scaling, unstable power-law exponents, and significantly fluctuating Taylor coefficients (variation in $β$ to be $Δβ= 0.51$). Moreover, SC-driven activity displays heavier-tailed distributions ($γ< 2$), indicating bursty and algorithm-driven activity. These findings reveal the characteristic differences between human-controlled and automated transaction behaviors in blockchain ecosystems. By uncovering universal scaling behaviors through the integration of complex systems theory and blockchain data analytics, this work provides a principled framework for understanding the underlying mechanisms of decentralized financial systems.
Emergency pharmaceutical logistics during rapid-onset disasters must balance timeliness, legal compliance, and environmental uncertainty. We present a hybrid framework that co-designs quantum-inspired decision dynamics, embedded legal constraints, and blockchain-verified environmental feedback. Candidate routes are modeled as a superposed state whose collapse is governed by entropy modulation-delaying commitment under ambiguity and accelerating resolution when coherent signals emerge. Legal statutes act as real-time projection operators shaping feasible choices, while environmental decoherence cues adjust confidence and path viability. The core engine is situated within a multilevel governance and mechanism design architecture, establishing clear roles, accountability channels, and audit trails. Large-scale simulations in wildfire scenarios demonstrate substantial gains over conventional baselines in latency, compliance, and robustness, while preserving interpretability and fairness adaptation. The resulting system offers a deployable, governance-aware infrastructure where law and physical risk jointly inform emergency routing decisions.
Ruixue Jing, Ryota Kobayashi, Luis Enrique Correa Rocha
The rapidly evolving cryptocurrency market presents unique challenges for investment due to its inherent volatility and evolving regulatory environment. Collective price movements can be exploited to construct diversified portfolios with improved risk-return profiles. This paper introduces an integrated framework that combines network analysis, price forecasting, and portfolio theory to identify stable groups of highly correlated cryptocurrencies for profitable portfolio construction. We employ the Louvain community detection algorithm together with consensus clustering to extract temporally persistent correlation clusters, and incorporate ARIMA-based price forecasts to enhance forward-looking cluster formation. Using 5 years of daily closing prices, we evaluate portfolio performance across multiple strategies and holding horizons, assessing both profitability and downside risk with return-based and tail-risk metrics. Our empirical results show that predictive consensus-clustering portfolios maintain consistently positive and stable performance up to a 14-day horizon, exhibit favourable gain-loss asymmetry, and achieve tighter tail-risk control. These findings demonstrate that stable interdependencies in cryptocurrency markets can be leveraged to construct profitable and risk-aware portfolios across short-term holding horizons.
Erveton P. Pinto, Marcelo A. Pires, Rone N. da Silva, Sı́lvio M. Duarte Queirós
We report the first application of a tailored Complexity-Entropy Plane designed for binary sequences and structures. We do so by considering the daily up/down price fluctuations of the largest cryptocurrencies in terms of capitalization (stable-coins excluded) that are worth $circa \,\, 90 \%$ of the total crypto market capitalization. With that, we focus on the basic elements of price motion that compare with the random walk backbone features associated with mathematical properties of the Efficient Market Hypothesis. From the location of each crypto on the Binary Complexity-Plane (BiCEP) we define an inefficiency score, $\mathcal I$, and rank them accordingly. The results based on the BiCEP analysis, which we substantiate with statistical testing, indicate that only Shiba Inu (SHIB) is significantly inefficient, whereas the largest stake of crypto trading is reckoned to operate in close-to-efficient conditions. Generically, our $\mathcal I$-based ranking hints the design and consensus architecture of a crypto is at least as relevant to efficiency as the features that are usually taken into account in the appraisal of the efficiency of financial instruments, namely canonical fiat money. Lastly, this set of results supports the validity of the binary complexity analysis.
Mélanie Chevance, J. M. Diederik Kruijssen, Steven N. Longmore
Astrophysics forms a cornerstone of human curiosity and has revolutionised our understanding of the Universe. However, conventional academic structures often hinder collaboration, transparency, and discovery. We present COOL Research DAO, a next-generation framework for cosmic origins astrophysics research that uses decentralised autonomous organisation (DAO) principles to make astrophysics research globally accessible, economically fair, and intellectually open. COOL Research DAO is designed to address four key systemic problems and their manifestations in traditional academic research: general inaccessibility, hierarchical organisation, unfair economic structures, and inefficient knowledge transfer. We describe how these inefficiencies can be addressed using blockchain-based tools and token systems. By fostering bottom-up governance, open-access knowledge networks, and transparent rewards, COOL Research DAO reshapes economic, organisational, and educational paradigms in astrophysics research. Our approach leverages the data-rich and inherently international nature of astrophysics, ensuring a scalable, collaborative platform that welcomes contributions ranging from computational analyses to public outreach. In doing so, we highlight a path toward realising our vision of a truly open research ecosystem, driven by community ownership, intellectual freedom, and shared fascination with our cosmic origins.
Ignacy Nieweglowski, Aviv Yaish, Fahad Saleh, Fan Zhang
Cryptoassets launched by political figures, e.g., political finance (PoliFi) tokens, have recently attracted attention. Chief among them are the eponymous tokens backed by the 47th president and first lady of the United States, TRUMPandMELANIA. We empirically analyze both, and study their impact on the broad decentralized finance (DeFi) ecosystem. Via a comparative longitudinal study, we uncover a "Trump Effect": the behavior of these tokens correlates positively with presidential approval ratings, whereas the same tight coupling does not extend to other cryptoassets and administrations. We additionally quantify the ecosystemic impact, finding that the fervor surrounding the two assets was accompanied by capital flows towards associated platforms like the Solana blockchain, which also enjoyed record volumes and fee expenditure.
Forks in the Bitcoin network result from the natural competition in the blockchain's Proof-of-Work consensus protocol. Their frequency is a critical indicator for the efficiency of a distributed ledger as they can contribute to resource waste and network insecurity. We introduce a model for the estimation of natural fork rates in a network of heterogeneous miners as a function of their number, the distribution of hash rates and the block propagation time over the peer-to-peer infrastructure. Despite relatively simplistic assumptions, such as zero propagation delay within mining pools, the model predicts fork rates which are comparable with the empirical stale blocks rate. In the past decade, we observe a reduction in the number of mining pools approximately by a factor 3, and quantify its consequences for the fork rate, whilst showing the emergence of a truncated power-law distribution in hash rates, justified by a rich-get-richer effect constrained by global energy supply limits. We demonstrate, both empirically and with the aid of our quantitative model, that the ratio between the block propagation time and the mining time is a sufficiently accurate estimator of the fork rate, but also quantify its dependence on the heterogeneity of miner activities. We provide empirical and theoretical evidence that both hash rate concentration and lower block propagation time reduce fork rates in distributed ledgers. Our work introduces a robust mathematical setting for investigating power concentration and competition on a distributed network, for interpreting discrepancies in fork rates -- for example caused by selfish mining practices and asymmetric propagation times -- thus providing an effective tool for designing future and alternative scenarios for existing and new blockchain distributed mining systems.
Quintino Francesco Lotito, Alberto Vendramini, Alberto Montresor, Federico Battiston
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within each hyperedge, and allow to account for the directional flow of information between nodes. Here, we provide a framework to characterize the structural organization of directed higher-order networks at their microscale. First, we extract the fingerprint of a directed hypergraph, capturing the frequency of hyperedges with a certain source and target sizes, and use this information to compute differences in higher-order connectivity patterns among real-world systems. Then, we formulate reciprocity in hypergraphs, including exact, strong, and weak definitions, to measure to which extent hyperedges are reciprocated. Finally, we extend motif analysis to identify recurring interaction patterns and extract the building blocks of directed hypergraphs. We validate our framework on empirical datasets, including Bitcoin transactions, metabolic networks, and citation data, revealing structural principles behind the organization of real-world systems.
Asim Ghosh, Soumyajyoti Biswas, Bikas K. Chakrabarti
We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the $Q$ factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices.
Mark C. Ballandies, Dino Carpentras, Evangelos Pournaras
Decentralized autonomous organizations (DAOs) have transformed organizational structures by shifting from traditional hierarchical control to decentralized approaches, leveraging blockchain and cryptoeconomics. Despite managing significant funds and building global networks, DAOs face challenges like declining participation, increasing centralization, and inabilities to adapt to changing environments, which stifle innovation. This paper explores DAOs as complex systems and applies complexity science to explain their inefficiencies. In particular, we discuss DAO challenges, their complex nature, and introduce the self-organization mechanisms of collective intelligence, digital democracy, and adaptation. By applying these mechanisms to refine DAO design and construction, a conceptual framework for assessing a DAO’s viability is created. This contribution lays the foundation for future research at the intersection of complexity science, digital democracy and DAOs.
Research on Bitcoin (BTC) transactions is a matter of interest for both economic and network science fields. Although this cryptocurrency is based on a decentralized system, making transaction details freely accessible, making raw blockchain data analyzable is not straightforward due to the Bitcoin protocol specificity and data richness. To address the need for an accessible dataset, we present ORBITAAL, the first comprehensive dataset based on temporal graph formalism. The dataset covers all Bitcoin transactions from January 2009 to January 2021. ORBITAAL provides temporal graph representations of entity-entity transaction networks, snapshots and stream graph. Each transaction value is given in Bitcoin and US dollar regarding daily-based conversion rate. This dataset also provides details on entities such as their global BTC balance and associated public addresses.
Financial networks can be constructed using statistical dependencies found within the price series of speculative assets. Across the various methods used to infer these networks, there is a general reliance on predictive modelling to capture cross-correlation effects. These methods usually model the flow of mean-response information, or the propagation of volatility and risk within the market. Such techniques, though insightful, don't fully capture the broader distribution-level causality that is possible within speculative markets. This paper introduces a novel approach, combining quantile regression with a piecewise linear embedding scheme - allowing us to construct causality networks that identify the complex tail interactions inherent to financial markets. Applying this method to 260 cryptocurrency return series, we uncover significant tail-tail causal effects and substantial causal asymmetry. We identify a propensity for coins to be self-influencing, with comparatively sparse cross variable effects. Assessing all link types in conjunction, Bitcoin stands out as the primary influencer - a nuance that is missed in conventional linear mean-response analyses. Our findings introduce a comprehensive framework for modelling distributional causality, paving the way towards more holistic representations of causality in financial markets.