The traditional Power Law model for Bitcoin is limited; it struggles to simultaneously fit historical data points across different eras without piecewise parameter adjustments. Bitcoin's trajectory is more naturally described as a tangent-based hyper-exponential system, driven by absolute supply scarcity.
Q-PROOF is an experimental blockchain architecture based on adaptive consensus, aperiodic topology, and quadratic governance. The model integrates Aperiodic Consensus Relaxation (ACR), distributed reputation, Sybil attack defense, coordinated attack detection, and post-quantum migration pathways. This technical white paper outlines the core consensus engine, mathematical modeling of system tension, correlation-aware consensus mechanics, and benchmark comparisons demonstrating enhanced finality and resilience against coordinated network capture.
Abstract Sybil attacks are a significant challenge in permissionless blockchains. However, existing research pays limited attention to how different modes of network evolution affect Sybil resistance. In practice, the method of node admission can greatly influence a blockchain’s resilience to Sybil attacks. To address this, we study Sybil resilience using a dynamic network growth model based on preferential attachment and adopt the Identity-Augmented Proof-of-Stake (IdAPoS) protocol as our consensus backbone. First, we extend IdAPoS with an on-chain Sybil-detection mechanism, reducing reliance on off-chain honesty assumptions. Subsequently, we formalize the network expansion procedure in IdAPoS by distinguishing the Applicant-based and Participant-based Network Expansion Models and assessing Sybil resistance under each model. Finally, using agent-based modeling, we simulate voting token value dynamics under Sybil attacks to quantify how expansion strategies affect Sybil resistance. Experiments show that our proposed trustworthiness-evaluation mechanism removes IdAPoS’s reliance on off-chain honesty information by extracting node-level Sybil-suspicion scores from on-chain voting relationships. Sybil attacks in blockchains cannot be eliminated but can only be delayed. Greater centralization among honest nodes generally strengthens Sybil resistance. Under superlinear network growth, the Participant-based Network Expansion Model achieves more stable scaling than the Applicant-based Network Expansion Model. Overall, IdAPoS improves system-level Sybil resilience at the cost of more centralized voting power.
The Bitcoin Lightning Network (LN) has emerged as a prominent Layer-2 solution de- signed to address the scalability limitations of the Bitcoin blockchain. However, as the network grows, understanding both its structural evolution and the reliability of its payment-routing mechanisms becomes increasingly important. This thesis investigates these two fundamental aspects through stochastic modeling and empirical analysis. First, we analyze the topological evolution of the Lightning Network. Empirical evi- dence reveals a persistent negative degree assortativity (disassortativity), a feature that classical generative models, such as the Barabási-Albert model, fail to reproduce asymp- totically. We introduce dynamic random graph models that extend preferential attach- ment by allowing edges to disappear over time at rates depending on node degree or channel capacity. We show that edge disappearance alone is sufficient to induce the disassortative mixing observed. Second, we address the reliability of payment routing in capacity-constrained networks inspired by the Lightning Network. We model the balance evolution of payment channels as a stochastic process governed by repeated routing of payments over shortest paths. By analyzing this process on both complete and general graphs, we derive upper and lower bounds for the time until the first payment failure occurs due to liquidity depletion. We establish that this failure time is governed by the ratio between the squared capacity of an edge and its betweenness centrality k2/g(e). Taken together, the results of this thesis provide principled insights into how decentral- ized payment networks evolve structurally in terms of topology and balance distributions
This paper examines Web3 ecosystems not merely as markets for digital assets, but as networked social spaces where economic transactions give rise to enduring social ties, shared narratives, and collective identities. Leveraging large-scale data mining of fused on-chain blockchain transactions and off-chain social media activity, we analyze over one hundred NFT collections to uncover how different forms of participation structure community formation in decentralized environments. Using network analysis, we identify distinct ecosystem roles, such as long-term holders, active traders, and short-term speculators, and demonstrate how each produces markedly different network topologies, levels of cohesion, and pathways for influence. We complement this structural analysis with discourse analysis of social media engagement, revealing how narrative production, visibility, and sustained interaction persist even as transactional activity declines. Our findings show that communities centered on holding behavior evolve from transactional networks into socially embedded ecosystems characterized by dense ties, decentralized influence, and ongoing cultural participation, while trader- and speculator-dominated networks remain fragmented and transactional. By linking network structure with discursive dynamics, this study provides a sociotechnical framework for understanding how value, identity, and inequality are negotiated in Web3 spaces. The approach offers a scalable method for detecting patterns of inclusion, exclusion, and representational imbalance, advancing network-based research on digital communities beyond purely economic or technical accounts.
This paper examines Web3 ecosystems not merely as markets for digital assets, but as networked social spaces where economic transactions give rise to enduring social ties, shared narratives, and collective identities. Leveraging large-scale data mining of fused on-chain blockchain transactions and off-chain social media activity, we analyze over one hundred NFT collections to uncover how different forms of participation structure community formation in decentralized environments. Using network analysis, we identify distinct ecosystem roles, such as long-term holders, active traders, and short-term speculators, and demonstrate how each produces markedly different network topologies, levels of cohesion, and pathways for influence. We complement this structural analysis with discourse analysis of social media engagement, revealing how narrative production, visibility, and sustained interaction persist even as transactional activity declines. Our findings show that communities centered on holding behavior evolve from transactional networks into socially embedded ecosystems characterized by dense ties, decentralized influence, and ongoing cultural participation, while trader- and speculator-dominated networks remain fragmented and transactional. By linking network structure with discursive dynamics, this study provides a sociotechnical framework for understanding how value, identity, and inequality are negotiated in Web3 spaces. The approach offers a scalable method for detecting patterns of inclusion, exclusion, and representational imbalance, advancing network-based research on digital communities beyond purely economic or technical accounts.
Bikki Kumar, Dev Karan, Adarsh Kandu, Ashish Khari
The social impact of decentralised online communities, such as blockchain-based social networks, is complex because their decentralisation allows users to exercise greater freedom and independence. A novel Dynamic Graph Neural Network with Temporal Knowledge Distillation (DGNN-TKD) is proposed to model and predict influence patterns. DGNN-TKD differs from standard Graph Neural Networks (GNNs), which function under the assumption of static graphs. It tracks the temporal evolution of a graph, and introduces a knowledge distillation mechanism that enables the transfer of influence embeddings over time. We propose a novel multi-dimensional influence metric that captures agent reputation, engagement and trust, supplemented with robust attention-based temporal aggregation. In experiments on decentralized social network datasets, DGNN-TKD surpasses current dynamic GNNs in influence prediction, community detection, and misinformation detection in decentralized governance/Web3 applications. This framework connects graph-based learning and social dynamics and serves as a powerful tool to study decentralized phenomena.
This paper extends the classical Avellaneda-Stoikov framework for optimal market making to blockchain networks with directed acyclic graph (DAG) structure. In DAG-based consensus protocols such as GHOSTDAG, multiple blocks are produced in parallel, creating a branching time structure that fundamentally alters the market maker's optimization problem. We derive a DAG-extended Hamilton-Jacobi-Bellman equation that incorporates the probability distribution over transaction acceptance, showing that optimal spreads depend on the anticipated ordering of parallel blocks. Our main theoretical result demonstrates that market makers achieve O(1/n) variance reduction in inventory risk by distributing quotes across n parallel execution paths, exploiting the transaction-level mutual exclusivity inherent to GHOSTDAG ordering. We extend the framework to K correlated assets (proving portfolio-level variance reduction of O(K/n)) and provide adversarial robustness analysis under bounded hash power attacks. Implementation analysis for the Kaspa network (10 BPS, k=124 post-Crescendo) addresses practical constraints including direct-to-miner submission requirements, fee incentive compatibility, and latency bounds. Monte Carlo simulations validate theoretical predictions, showing Sharpe ratio improvements of 40-82% over single-path strategies under realistic network conditions. This work establishes foundational theory for high-frequency decentralized finance applications on DAG-based blockchains.
Decentralized Finance (DeFi) has rapidly emerged as one of the most transformative applications of blockchain technology, enabling permissionless financial services including lending, borrowing, trading, and yield optimization through smart contract-based protocols. The complex interactions among users, protocols, and assets in the DeFi ecosystem naturally form intricate graph structures whose topology encodes critical information about system behavior, risk propagation, and economic vulnerabilities. This paper presents a comprehensive survey of graph-based analytical methods applied to the DeFi ecosystem. We systematically review transaction graphs, protocol dependency graphs, liquidity flow networks, and user interaction graphs, examining how graph-theoretic techniques-including community detection, centrality analysis, temporal graph mining, and anomaly detection-have been applied to understand DeFi dynamics. We further analyze how graph methods reveal systemic risks such as composability-induced contagion, flash loan attack patterns, and liquidity concentration. We propose a unified DeFi Graph Analysis Taxonomy (DGAT) that classifies existing work across graph construction methodologies, analytical objectives, and application domains. Comparative evaluation of current approaches identifies key research gaps and outlines directions for future investigation, particularly in cross-protocol risk modeling and real-time graph analytics for DeFi monitoring.
Wassim Sliti, Félix Cuadrado, Leandro Campos Hernáez, Juan C. Dueñas
Illicit activities and coordinated manipulations in the Non-Fungible Tokens (NFT) market remain significant concerns, driven by the pseudonymous and publicly transparent nature of blockchain transactions and the lack of market oversight. In this study, we introduce a novel framework for detecting suspicious behavior in NFT trading ecosystems through temporal graph analysis. Our approach represents the market as a large-scale, time-evolving transactional graph, capturing realistic market dynamics and the complex interactions between traders.By leveraging temporal graphs, we track not only connections between traders but also the evolution of these interactions over time, including their sequence, rhythm, and frequency, enabling the identification of anomalous behaviors that static graph representations cannot reveal and that may warrant further examination. Using an optimized temporal cycle-detection algorithm, we extract connected groups of wallets for in-depth behavioral analysis, uncovering patterns indicative of unusual coordinated manipulation. To overcome the absence of labeled ground-truth validation data, we employ a temporal motif–based validation, demonstrating that flagged entities exhibit trading behaviors significantly deviating from standard market dynamics. Our results highlight the potential of temporal graph–based methodologies to provide a scalable and effective risk-profiling and market-surveillance tool, assisting analysts and regulatory entities in narrowing the investigation space within the large, permissionless NFT markets and enhancing surveillance, risk detection, and regulatory oversight in decentralized NFT markets.
Baoyu Zhang, Tao Chen, Weishan Zhang, Tao Wang · 9 authors
In September 2024, Lebanon was rocked by an unprecedented cyber-physical attack using Pager bombs. The attack combined advanced cyber warfare techniques with physical destruction, resulting in significant loss of life, infrastructure damage, and geopolitical repercussions. In this paper, we analyze the attitudes on this attack, from both English and Arabic social media users, and investigate impacts on global electronic devices sales and usage. A new topic discovery approach using large models and small models collaboration is proposed. We compare English and Arabic topics generated on social media and find that people in different language spaces share common topics of anxiety on this event. By analyzing market share trends in both China and the United States, an obvious correlation can be found between this event and phone sales. In addition, we discuss the evolution of warfare, and how DAOs(Decentralized Autonomous Organizations) can be utilized to improve the security of electronic devices by secured monitoring of their whole lifecycle.
Web3 technologies, notably Non-Fungible Tokens (NFTs) and Decentralized Finance (DeFi), have generated extensive social media discourse. This study integrates Social Network Analysis (SNA) and BERTopic to examine spreader roles in shaping Web3 conversations on platform X. We collected 12,925 NFT and 7,087 DeFi posts from August 23 to September 23, 2025, using domain-specific keywords. Data preprocessing removed duplicates, spam, and irrelevant content through URL stripping, hashtag filtering, and manual verification of top spreaders to exclude automated accounts. All collection adhered to X's Terms of Service using publicly available English-language posts without personal identifying information. In-degree centrality analysis identified top spreaders. @GiveRep in NFT achieved a time reached of 288 hours with an average propagation speed of two hours, while @BioProtocol in DeFi demonstrated a uniform persistence of 192 hours uniform persistence across top actors. BERTopic analysis revealed thematic differences. NFT discussions centered on community engagement and speculation, whereas DeFi discourse concentrated on protocol infrastructure and yield mechanisms. NFT spreaders exhibited varied influence duration aligned with thematic diversity, while DeFi spreaders showed uniform persistence constrained by content overlap. This integrated framework advances computational social research methodologies and offers practical insights for Web3 stakeholders to identify key influencers and optimize community engagement strategies. Limitations include single-platform focus and one-month observation period.
Airdrops are a widely used mechanism in Web3 ecosystems to incentivize early users by distributing governance tokens. However, these mechanisms are increasingly targeted by airdrop hunters—malicious actors who exploit token distribution systems through address farming, automated scripts, and behavioral camouflage. While prior work such as ARTEMIS leverages multimodal features and local transaction patterns to detect such behavior, it lacks a global understanding of wallet influence in the transaction graph. In this paper, we propose an enhanced detection framework that augments the ARTEMIS by incorporating PageRank-based global centrality as an additional structural feature. This allows the model to better distinguish superficially active wallets from those with broader influence in the network. We evaluate our method on real-world Non-Fungible Token (NFT) data from the Blur marketplace and achieve state-of-the-art performance. Furthermore, a feature substitution experiment reveals that simple degree-based features alone can achieve near-perfect performance, even outperforming PageRank, suggesting that the labels are strongly coupled with topological properties. These findings highlight both the effectiveness of structural augmentation and the potential risks of shortcut learning in graph-based detection systems.
We introduce multiscale topological analysis for studying cryptocurrency price series in the time domain. This is achieved by first performing a coarse-grained procedure on the volatility series at multiple temporal scales, and then constructing consecutive visibility graphs from the resulting coarse-grained series. We show that their degree distribution presents a likely power-law behavior. This scaling characteristics keeps invariant even varying time scale factor. Interestingly, we find that the number of cliques that capturing higher-order relations, presents a clear power-law behavior with the time scale factor. Their associated scaling exponent shows a monotonically decreasing pattern. Our work reveals the function of higher-order topological structure underlying cryptocurrency time series.
Decentralization has an important geographic dimension that conventional metrics, such as stake distribution, often overlook. Where validators operate affects resilience to regional shocks (e.g., outages, natural disasters, or government intervention) as well as fairness in reward access. Yet major blockchain protocols do not encode geographical location in their rules; instead, validator locations emerge from a combination of economic incentives, regulatory constraints, infrastructure availability, and validator deployment choices. When certain locations offer systematic advantages, validators may strategically co-locate to maximize expected rewards, as observed in Ethereum, where validators cluster along the Atlantic corridor, which exhibits favorable latency. In this paper, we propose a formal model of validators' geographical positioning incentives under Ethereum's protocol design, capturing the interaction between its two block-building paradigms, local and external block building, and the geographical distribution of validators and information sources. We analytically characterize the model under a mean-field approximation and complement this analysis with an agent-based simulation calibrated with real-world latency data to quantify how these incentives translate into geographical concentration under heterogeneous geographic and infrastructural conditions. Our results show that Ethereum's block-building architecture is not geographically neutral. Both paradigms generate location-dependent payoffs and incentives to relocate closer to payoff-relevant parties in order to reduce propagation delays, although through different underlying mechanisms. Asymmetric access to information sources further amplifies geographical centralization. We also demonstrate that consensus parameters, such as attestation thresholds and slot times, modulate latency sensitivity and can amplify these effects, acting as protocol-level levers. Finally, we discuss the implications of our findings for protocol design and outline potential mitigation directions informed by our analysis.
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.
Marcin Wątorek, Marija Bezbradica, Martin Crane, Jarosław Kwapień · 5 authors
Based on the cryptocurrency market dynamics, this study presents a general methodology for analyzing evolving correlation structures in complex systems using the $q$-dependent detrended cross-correlation coefficient ρ(q,s). By extending traditional metrics, this approach captures correlations at varying fluctuation amplitudes and time scales. The method employs $q$-dependent minimum spanning trees ($q$MSTs) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (Jan 2021-Oct 2024), a rolling window analysis reveals significant shifts in $q$MSTs, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum (ETH) and others gaining prominence. Spectral analysis confirms BTC's declining dominance and increased diversification among assets. A key finding is that medium-scale fluctuations exhibit stronger correlations than large-scale ones, with $q$MSTs based on the latter being more decentralized. Properly exploiting such facts may offer the possibility of a more flexible optimal portfolio construction. Distance metrics highlight that major disruptions amplify correlation differences, leading to fully decentralized structures during crashes. These results demonstrate $q$MSTs' effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems.
With the rise of cryptocurrencies, illicit activities such as money laundering, fraud, and Ponzi schemes have gained attention. Traditional methods using graph neural networks (GNNs) to detect illicit transactions treat the entire transaction network as input, which works well on small networks but struggles with large-scale blockchain data. To address this limitation, the authors propose a neighborhood subgraph-based method that combines GCN and LSTM. The GCN captures information from neighboring nodes for each transaction, enhancing the understanding of the network structure, while the LSTM tracks the sequence and variations of fund flows. Experimental results show that by using 3-hop neighborhood subgraphs, the method outperforms other baseline models while requiring data from only an average of 80 nodes, thereby significantly improving efficiency compared to methods that process the entire transaction network.