Finance networks and supply chains

The network structure of real-world supply chains inherently carries a vulnerability to systemic risk. Local shocks can escalate into widespread disruptions due to the high level of interdependence between firms. While recent advances have made it possible to quantify systemic risk in production networks, how different network topologies of supply links contribute to this risk remains unclear. To address this question, we employ a method inspired by statistical physics that allows us to find network configurations with minimal systemic risk while respecting firm-level constraints to production. Analyzing six subnetworks derived from Hungary's and Ecuador's countrywide production networks, we demonstrate that the systemic risk can be significantly mitigated without impacting the volume of traded goods or firms' production output. A comparison of the network properties before and after our optimal rewiring indicates that this result is achieved by changing the connectivity in a non-trivial way. These results suggest that production network topologies are suboptimal as they carry a level of risk much larger than is necessary in order to sustain production. Our findings provide new insights to devise policies seeking to reduce systemic risk through targeted interventions in supply chain networks.

The level of systemic risk in economic and financial systems is strongly determined by the structure of the underlying networks of interdependent entities that can propagate shocks and stresses. Since changes in network structure imply changes in risk levels, it is important to identify structural transitions potentially leading to system-wide crises. Methods have been proposed to assess whether a real-world network is in a (quasi-)stationary state by checking the consistency of its structural evolution with appropriate maximum-entropy ensembles of graphs. While previous analyses of this kind have focused on dyadic and triadic motifs, hence disregarding higher-order structures, here we consider closed walks of any length. Specifically, we study the ensemble properties of the spectral radius of random graph models calibrated on real-world evolving networks. Our approach is shown to work remarkably well for directed networks, both binary and weighted. As illustrative examples, we consider the Electronic Market for Interbank Deposit (e-MID), the Dutch Interbank Network (DIN) and the International Trade Network (ITN) in their evolution across the 2008 crisis. By monitoring the deviation of the spectral radius from its ensemble expectation, we find that the ITN remains in a (quasi-)equilibrium state throughout the period considered, while both the DIN and e-MID exhibit a clear out-of-equilibrium behaviour. The spectral deviation therefore captures ongoing topological changes, extending over all length scales, to provide a compact proxy of the resilience of economic and financial networks.

The international trade of food products plays an important role in maintaining food security across the globe. However, food trade has changed over time, adapting to political maneuvers, globalization, and even climatic shocks. Comprehending the temporal evolution of food trade networks, and how such changes condition the system's robustness can be very valuable for designing effective interventions against future crises. To this end, we studied the temporal evolution of global food trade networks and characterized how their topological and functional robustness changed between 1986-2021. For each year, we built a multiplex representation of the trade relationships between 219 countries across 12 food categories (defined based on 216 individual products [1]). We then explored the temporal evolution of several multiplex network metrics (e.g. participation coefficient, weighted overlap, inverse participation ratio) to identify trends that could influence network robustness to shocks. Overall, we observed that countries have experienced simultaneously an increase in globalization (dependence on imports) and an increase in export diversification. This export diversification is not uniform across products, with some products exhibiting an increase in regionalization (``Animal and vegetal), while others becoming more decentralized (``Grain and derived products"). Such heterogeneities may generate discrepancies in each layer's robustness to production shocks. To test it, we simulated the impact of single-country production shocks in different years. Using a shock model inspired by [2], we evaluated the changes in shock size, the most affected countries, and the main shock producers. In the case of grain products, though the maximal cascade size generated remains similar between 1986 and 2019, there is an increase in the number of countries that could potentially cause large cascades...

Modern global trade networks are characterized by complex interdependencies, making supply chain stability for critical commodities a key concern. Expanding the range of trade partners may seem like a straightforward way to enhance resilience, but it can still leave countries exposed if partners rely on the same upstream suppliers. This highlights the need for a more comprehensive approach that traces commodities from their sources to final consumption.We adapt the power tracing technique from electrical grid analysis [1] to address this issue. Originally designed to quantify dependencies between generators and consumers by analyzing electricity flows, we apply this concept to trace commodity pathways in global trade. Using a Markov chain model, our framework simulates the flow of goods and reconstructs observed trade distributions, revealing risks and structural dependencies. We further develop a multilayer framework linking commodity flows across stages of production.We demonstrate the framework's utility through its application to Lithium-Ion Batteries (LIBs) for electric vehicles (EVs). By tracing materials like lithium from mining to final consumption, we identify supply chains balancing route diversity with environmental and human rights standards. This perspective reveals key vulnerabilities and offers strategic guidance for resilient trade portfolios. At the global level, it pinpoints critical hubs and potential failure points that could disrupt supply chains. Incorporating raw materials, intermediate goods, and final products, our method provides a unified framework for analyzing interdependencies and their impacts.

Inter-firm networks have been shown to play a crucial role in the propagation and amplification of economic shocks at the national level: as such, knowledge of these systems is of capital importance in order to properly address economic resilience to disruptive events. Comprehensive data about supply chains is, however, seldom available, triggering a flourishing literature about reconstruction models, aimed at predicting the most probable configurations of these networks starting from the partial, available, information. In this work we test different network reconstruction models rooted in the Maximum Entropy framework, namely the stripe-corrected Gravity Model (scGM), the Input-Output scGM (IO scGM), introduced in the paper, and the density-corrected Gravity Model (dcGM), on the reconstruction the Ecuadorian production network, accessed through a unique dataset provided by the Ecuadorian Tax Office. Differently from previous reconstruction attempts, here we focus on the ability of the models to correctly identify firm-level systemic risk, as measured by ESRI. The scGM displays the best overall reconstruction performance, proving to be able to generate reliable synthetic networks both from a structural and from an economic point of view, despite requiring very limited information on the empirical network (namely the sector-specific in- and out-strength of firms): when this information is not available, it can be well approximated by the fluxes between industrial sectors, as in the IO scGM. Our findings shed light on the minimal amount of empirical information that is needed in order to generate realistic synthetic production networks, able to capture the systemic risk of an economy.

Digital twins are virtual replicas of real-world systems, enabling the study of economic and financial systems while preserving data confidentiality. We propose a framework for building digital twins tailored to these systems, using Exponential Random Graph Models (ERGMs) turned into fitness-based, generative models. These models capture structural features while abstracting sensitive data, enabling secure data sharing and promoting reproducibility in economic and financial network studies. Fitness-based ERGMs transform constraints like degree distribution moments into measurable properties such as economic size or trade volume.We analyze linear models (e.g., the Configuration Model) and non-linear models (e.g., the Two-Star and Degree-Corrected Two-Star Models) on e-MID, the Dutch Interbank Network, and the International Trade Network (ITN), focusing on their evolution during the 2008 crisis. The fitness-induced Configuration Model \emph{i)} solves quickly via the fixed point of its induced map; \emph{ii)} reproduces node degrees accurately; and \emph{iii)} induces a core-periphery structure, though it underestimates degree variance.To address this, we studied non-linear models like the Two-Star and Degree-Corrected Two-Star Models (solved via mean-field approximation). By constraining two-stars (V-motifs), these models address degree variance. For the ITN in 2000, the Two-Star Model overestimates degree variance, while the Degree-Corrected Two-Star Model provides closer estimates but adds little value over the simpler Configuration Model. This reflects the ITN’s dependence on node degrees, confirmed by the Bayesian Information Criterion.Our goal is to create accurate virtual replicas of economic and financial systems to assess systemic risk and plan policies while preserving data privacy. Reproducing the second moment of the degree distribution remains crucial to this aim.