Graph Theory

Needles in a haystack: using forensic network science to uncover insider trading ArXiv ID: 2512.18918 “View on arXiv” Authors: Gian Jaeger, Wang Ngai Yeung, Renaud Lambiotte Abstract Although the automation and digitisation of anti-financial crime investigation has made significant progress in recent years, detecting insider trading remains a unique challenge, partly due to the limited availability of labelled data. To address this challenge, we propose using a data-driven networks approach that flags groups of corporate insiders who report coordinated transactions that are indicative of insider trading. Specifically, we leverage data on 2.9 million trades reported to the U.S. Securities and Exchange Commission (SEC) by company insiders (C-suite executives, board members and major shareholders) between 2014 and 2024. Our proposed algorithm constructs weighted edges between insiders based on the temporal similarity of their trades over the 10-year timeframe. Within this network we then uncover trends that indicate insider trading by focusing on central nodes and anomalous subgraphs. To highlight the validity of our approach we evaluate our findings with reference to two null models, generated by running our algorithm on synthetic empirically calibrated and shuffled datasets. The results indicate that our approach can be used to detect pairs or clusters of insiders whose behaviour suggests insider trading and/or market manipulation. ...

Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks ArXiv ID: 2507.03963 “View on arXiv” Authors: Yen Jui Chang, Wei-Ting Wang, Yun-Yuan Wang, Chen-Yu Liu, Kuan-Cheng Chen, Ching-Ray Chang Abstract Financial markets are noisy yet contain a latent graph-theoretic structure that can be exploited for superior risk-adjusted returns. We propose a quantum stochastic walk (QSW) optimizer that embeds assets in a weighted graph: nodes represent securities while edges encode the return-covariance kernel. Portfolio weights are derived from the walk’s stationary distribution. Three empirical studies support the approach. (i) For the top 100 S&P 500 constituents over 2016-2024, six scenario portfolios calibrated on 1- and 2-year windows lift the out-of-sample Sharpe ratio by up to 27% while cutting annual turnover from 480% (mean-variance) to 2-90%. (ii) A $5^{“4”}=625$-point grid search identifies a robust sweet spot, $α,λ\lesssim0.5$ and $ω\in[“0.2,0.4”]$, that delivers Sharpe $\approx0.97$ at $\le 5%$ turnover and Herfindahl-Hirschman index $\sim0.01$. (iii) Repeating the full grid on 50 random 100-stock subsets of the S&P 500 adds 31,350 back-tests: the best-per-draw QSW beats re-optimised mean-variance on Sharpe in 54% of cases and always wins on trading efficiency, with median turnover 36% versus 351%. Overall, QSW raises the annualized Sharpe ratio by 15% and cuts turnover by 90% relative to classical optimisation, all while respecting the UCITS 5/10/40 rule. These results show that hybrid quantum-classical dynamics can uncover non-linear dependencies overlooked by quadratic models and offer a practical, low-cost weighting engine for themed ETFs and other systematic mandates. ...

A Line Graph-Based Framework for Identifying Optimal Routing Paths in Decentralized Exchanges ArXiv ID: 2504.15809 “View on arXiv” Authors: Unknown Abstract Decentralized exchanges, such as those employing constant product market makers (CPMMs) like Uniswap V2, play a crucial role in the blockchain ecosystem by enabling peer-to-peer token swaps without intermediaries. Despite the increasing volume of transactions, there remains limited research on identifying optimal trading paths across multiple DEXs. This paper presents a novel line-graph-based algorithm (LG) designed to efficiently discover profitable trading routes within DEX environments. We benchmark LG against the widely adopted Depth-First Search (DFS) algorithm under a linear routing scenario, encompassing platforms such as Uniswap, SushiSwap, and PancakeSwap. Experimental results demonstrate that LG consistently identifies trading paths that are as profitable as, or more profitable than, those found by DFS, while incurring comparable gas costs. Evaluations on Uniswap V2 token graphs across two temporal snapshots further validate LG’s performance. Although LG exhibits exponential runtime growth with respect to graph size in empirical tests, it remains viable for practical, real-world use cases. Our findings underscore the potential of the LG algorithm for industrial adoption, offering tangible benefits to traders and market participants in the DeFi space. ...

Hierarchical Minimum Variance Portfolios: A Theoretical and Algorithmic Approach ArXiv ID: 2503.12328 “View on arXiv” Authors: Unknown Abstract We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by Lopez de Prados hierarchical risk parity and Cottons Schur complement methods, our framework models the covariance matrix as an adjacency-like structure of a hierarchical graph. We demonstrate that portfolio optimization can be recursively reduced across hierarchical levels, allowing optimal weights to be computed efficiently by inverting only small submatrices regardless of portfolio size. Moreover, we translate our results into a recursive algorithm that constructs optimal portfolio allocations. Our results reveal a transparent and mathematically rigorous connection between classical Markowitz mean-variance optimization, hierarchical clustering, and the Schur complement method. ...

Dynamical analysis of financial stocks network: improving forecasting using network properties ArXiv ID: 2408.11759 “View on arXiv” Authors: Unknown Abstract Applying a network analysis to stock return correlations, we study the dynamical properties of the network and how they correlate with the market return, finding meaningful variables that partially capture the complex dynamical processes of stock interactions and the market structure. We then use the individual properties of stocks within the network along with the global ones, to find correlations with the future returns of individual S&P 500 stocks. Applying these properties as input variables for forecasting, we find a 50% improvement on the R2score in the prediction of stock returns on long time scales (per year), and 3% on short time scales (2 days), relative to baseline models without network variables. ...

TCGPN: Temporal-Correlation Graph Pre-trained Network for Stock Forecasting ArXiv ID: 2407.18519 “View on arXiv” Authors: Unknown Abstract Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many Temporal-correlation Forecasting Problem. However, when applied to tasks lacking periodicity, such as stock data prediction, the effectiveness and robustness of STGNNs are found to be unsatisfactory. And STGNNs are limited by memory savings so that cannot handle problems with a large number of nodes. In this paper, we propose a novel approach called the Temporal-Correlation Graph Pre-trained Network (TCGPN) to address these limitations. TCGPN utilize Temporal-correlation fusion encoder to get a mixed representation and pre-training method with carefully designed temporal and correlation pre-training tasks. Entire structure is independent of the number and order of nodes, so better results can be obtained through various data enhancements. And memory consumption during training can be significantly reduced through multiple sampling. Experiments are conducted on real stock market data sets CSI300 and CSI500 that exhibit minimal periodicity. We fine-tune a simple MLP in downstream tasks and achieve state-of-the-art results, validating the capability to capture more robust temporal correlation patterns. ...

Information Flow in the FTX Bankruptcy: A Network Approach ArXiv ID: 2407.12683 “View on arXiv” Authors: Unknown Abstract This paper investigates the cryptocurrency network of the FTX exchange during the collapse of its native token, FTT, to understand how network structures adapt to significant financial disruptions, by exploiting vertex centrality measures. Using proprietary data on the transactional relationships between various cryptocurrencies, we construct the filtered correlation matrix to identify the most significant relations in the FTX and Binance markets. By using suitable centrality measures - closeness and information centrality - we assess network stability during FTX’s bankruptcy. The findings document the appropriateness of such vertex centralities in understanding the resilience and vulnerabilities of financial networks. By tracking the changes in centrality values before and during the FTX crisis, this study provides useful insights into the structural dynamics of the cryptocurrency market. Results reveal how different cryptocurrencies experienced shifts in their network roles due to the crisis. Moreover, our findings highlight the interconnectedness of cryptocurrency markets and how the failure of a single entity can lead to widespread repercussions that destabilize other nodes of the network. ...

Portfolio management using graph centralities: Review and comparison ArXiv ID: 2404.00187 “View on arXiv” Authors: Unknown Abstract We investigate an application of network centrality measures to portfolio optimization, by generalizing the method in [“Pozzi, Di Matteo and Aste, \emph{“Spread of risks across financial markets: better to invest in the peripheries”}, Scientific Reports 3:1665, 2013”], that however had significant limitations with respect to the state of the art in network theory. In this paper, we systematically compare many possible variants of the originally proposed method on S&P 500 stocks. We use daily data from twenty-seven years as training set and their following year as test set. We thus select the best network-based methods according to different viewpoints including for instance the highest Sharpe Ratio and the highest expected return. We give emphasis in new centrality measures and we also conduct a thorough analysis, which reveals significantly stronger results compared to those with more traditional methods. According to our analysis, this graph-theoretical approach to investment can be used successfully by investors with different investment profiles leading to high risk-adjusted returns. ...

Pairs Trading Using a Novel Graphical Matching Approach ArXiv ID: 2403.07998 “View on arXiv” Authors: Unknown Abstract Pairs trading, a strategy that capitalizes on price movements of asset pairs driven by similar factors, has gained significant popularity among traders. Common practice involves selecting highly cointegrated pairs to form a portfolio, which often leads to the inclusion of multiple pairs sharing common assets. This approach, while intuitive, inadvertently elevates portfolio variance and diminishes risk-adjusted returns by concentrating on a small number of highly cointegrated assets. Our study introduces an innovative pair selection method employing graphical matchings designed to tackle this challenge. We model all assets and their cointegration levels with a weighted graph, where edges signify pairs and their weights indicate the extent of cointegration. A portfolio of pairs is a subgraph of this graph. We construct a portfolio which is a maximum weighted matching of this graph to select pairs which have strong cointegration while simultaneously ensuring that there are no shared assets within any pair of pairs. This approach ensures each asset is included in just one pair, leading to a significantly lower variance in the matching-based portfolio compared to a baseline approach that selects pairs purely based on cointegration. Theoretical analysis and empirical testing using data from the S&P 500 between 2017 and 2023, affirm the efficacy of our method. Notably, our matching-based strategy showcases a marked improvement in risk-adjusted performance, evidenced by a gross Sharpe ratio of 1.23, a significant enhancement over the baseline value of 0.48 and market value of 0.59. Additionally, our approach demonstrates reduced trading costs attributable to lower turnover, alongside minimized single asset risk due to a more diversified asset base. ...

Exploring the Bitcoin Mesoscale ArXiv ID: 2307.14409 “View on arXiv” Authors: Unknown Abstract The open availability of the entire history of the Bitcoin transactions opens up the possibility to study this system at an unprecedented level of detail. This contribution is devoted to the analysis of the mesoscale structural properties of the Bitcoin User Network (BUN), across its entire history (i.e. from 2009 to 2017). What emerges from our analysis is that the BUN is characterized by a core-periphery structure a deeper analysis of which reveals a certain degree of bow-tieness (i.e. the presence of a Strongly-Connected Component, an IN- and an OUT-component together with some tendrils attached to the IN-component). Interestingly, the evolution of the BUN structural organization experiences fluctuations that seem to be correlated with the presence of bubbles, i.e. periods of price surge and decline observed throughout the entire Bitcoin history: our results, thus, further confirm the interplay between structural quantities and price movements observed in previous analyses. ...