Aou(n), where an output address au receives Aou(n) coins. On the Bitcoin network, an address may appear multiple times with different inputs and outputs. An address u that appears in a transaction at time t can be denoted as atu. Thenumberofblocksmeasuresthe speed in the 24-hour window that contains a transaction involving the coin. Second, temporal information of transactions, such as the local time, has been useful to cluster criminal transactions.

However, analyzing blockchain data requires domain expertise and computational resources, which pose a significant barrier and hinder advancement in this field.

Numerous studies have been conducted to investigate the properties of large-scale temporal graphs. Despite the ubiquity of these graphs in real-world scenarios, it's usually impractical for us to obtain the whole real-time graphs due to privacy concerns and technical limitations. In this paper, we introduce the concept of {\it Live Graph Lab} for temporal graphs, which enables open, dynamic and real transaction graphs from blockchains. Among them, Non-fungible tokens (NFTs) have become one of the most prominent parts of blockchain over the past several years. With more than \$40 billion market capitalization, this decentralized ecosystem produces massive, anonymous and real transaction activities, which naturally forms a complicated transaction network. However, there is limited understanding about the characteristics of this emerging NFT ecosystem from a temporal graph analysis perspective.

We propose a novel QTGNN framework for detecting fraudulent transactions in large-scale financial networks. By integrating quantum embedding, variational graph convolutions, and topological data analysis, QTGNN captures complex transaction dynamics and structural anomalies indicative of fraud. The methodology includes quantum data embedding with entanglement enhancement, variational quantum graph convolutions with non-linear dynamics, extraction of higher-order topological invariants, hybrid quantum-classical anomaly learning with adaptive optimization, and interpretable decision-making via topological attribution. Rigorous convergence guarantees ensure stable training on noisy intermediate-scale quantum (NISQ) devices, while stability of topological signatures provides robust fraud detection. Optimized for NISQ hardware with circuit simplifications and graph sampling, the framework scales to large transaction networks. Simulations on financial datasets, such as PaySim and Elliptic, benchmark QTGNN against classical and quantum baselines, using metrics like ROC-AUC, precision, and false positive rate. An ablation study evaluates the contributions of quantum embeddings, topological features, non-linear channels, and hybrid learning. QTGNN offers a theoretically sound, interpretable, and practical solution for financial fraud detection, bridging quantum machine learning, graph theory, and topological analysis.

Due to the decentralized nature of blockchain, this makes it possible for everyone to access all the transaction information.

Purpose: This paper introduces a novel graph-based method, GARG-AML, for efficient and effective anti-money laundering (AML). It quantifies smurfing risk, a popular money laundering method, by providing each node in the network with a single interpretable score. The proposed method strikes a balance among computational efficiency, detection power and transparency. Different versions of GARG-AML are introduced for undirected and directed networks. Methodology: GARG-AML constructs the adjacency matrix of a node's second-order neighbourhood in a specific way. This allows us to use the density of different blocks in the adjacency matrix to express the neighbourhood's resemblance to a pure smurfing pattern. GARG-AML is extended using a decision tree and gradient-boosting classifier to increase its performance even more. The methods are tested on synthetic and on open-source data against the current state-of-the-art in AML. Findings: We find that GARG-AML obtains state-of-the-art performance on all datasets. We illustrate that GARG-AML scales well to massive transactions graphs encountered at financial institutions. By leveraging only the adjacency matrix of the second-order neighbourhood and basic network features, this work highlights the potential of fundamental network properties towards advancing fraud detection. Originality: This paper uses only basic network features and expert knowledge on smurfing to construct a performant AML system. The originality lies in the translation of smurfing detection to these features and network representation. Our proposed method is built around the real business needs of scalability and interpretability. It therefore provides a solution that can be easily implemented at financial institutions or incorporated in existing AML solutions.

Money laundering enables organized crime by moving illicit funds into the legitimate economy. Although trillions of dollars are laundered each year, detection rates remain low because launderers evade oversight, confirmed cases are rare, and institutions see only fragments of the global transaction network. Since access to real transaction data is tightly restricted, synthetic datasets are essential for developing and evaluating detection methods. However, existing datasets fall short: they often neglect partial observability, temporal dynamics, strategic behavior, uncertain labels, class imbalance, and network-level dependencies. We introduce AMLGentex, an open-source suite for generating realistic, configurable transaction data and benchmarking detection methods. AMLGentex enables systematic evaluation of anti-money laundering systems under conditions that mirror real-world challenges. By releasing multiple country-specific datasets and practical parameter guidance, we aim to empower researchers and practitioners and provide a common foundation for collaboration and progress in combating money laundering.