Dissortative From the Outside, Assortative From the Inside: Social Structure and Behavior in the Industrial Trade Network

It is generally accepted that neighboring nodes in financial networks are negatively assorted with respect to the correlation between their degrees. This feature would play an important ‘damping’ role in the market during downturns (periods of distress) since this connectivity pattern between firms lowers the chances of auto-amplifying (the propagation of) distress. In this paper we explore a trade-network of industrial firms where the nodes are suppliers or buyers, and the links are those invoices that the suppliers send out to their buyers and then go on to present to their bank for discounting. The network was collected by a large Italian bank in 2007, from their intermediation of the sales on credit made by their clients. The network also shows dissortative behavior as seen in other studies on financial networks. However, when looking at the credit rating of the firms, an important attribute internal to each node, we find that firms that trade with one another share overwhelming similarity. We know that much data is missing from our data set. However, we can quantify the amount of missing data using information exposure, a variable that connects social structure and behavior. This variable is a ratio of the sales invoices that a supplier presents to their bank over their total sales. Results reveal a non-trivial and robust relationship between the information exposure and credit rating of a firm, indicating the influence of the neighbors on a firm’s rating. This methodology provides a new insight into how to reconstruct a network suffering from incomplete information.

💡 Research Summary

The paper investigates an industrial trade‑credit network built from data collected by a large Italian bank in 2007. Nodes represent firms (suppliers or buyers) and directed edges correspond to invoices that suppliers submit to the bank for discounting. The authors first confirm that, with respect to degree, the network exhibits the classic disassortative pattern observed in many financial systems: high‑degree suppliers are linked to many low‑degree buyers, the in‑degree distribution follows a power‑law over six orders of magnitude, while the out‑degree distribution is approximately log‑normal. This topology is often cited as a “damping” mechanism that reduces the probability of rapid contagion during crises.

However, when the internal attribute of credit rating (a score from 1 = most credit‑worthy to 9 = most credit‑constrained) is taken into account, a strikingly opposite pattern emerges. Firms tend to trade with partners that have very similar credit ratings, producing a strong assortative mixing by this attribute. The authors group ratings into three classes (A = 1‑3, B = 4‑6, C = 7‑9) and show that intra‑class links dominate while inter‑class connections are scarce. This dual structure—disassortative by degree but assortative by credit rating—implies that systemic risk may be concentrated within rating cohorts even though the overall network appears robust.

A major methodological contribution is the introduction of “information exposure” (denoted a), defined as the ratio of the total face value of invoices a supplier presents to the bank to its total annual net‑sales (derived from balance‑sheet data). This variable captures how much a firm relies on bank‑mediated discounting for liquidity. Empirical analysis reveals a non‑linear, robust relationship between information exposure and credit rating: lower‑rated (higher‑risk) firms exhibit markedly higher exposure, while higher‑rated firms keep exposure low, presumably because they can obtain financing through other channels. The relationship is especially pronounced in the middle rating range, suggesting a transition in financing behavior.

The dataset is heavily biased: the bank preferentially serves large, credit‑worthy suppliers, and only records transactions that pass through its discounting platform. Consequently, many links—particularly those involving small firms or alternative financing arrangements—are missing not at random. Rather than imputing missing links randomly or relying on strong Bayesian priors, the authors exploit the observed exposure‑rating relationship to infer the amount of hidden activity. By comparing the expected exposure for a given rating class with the observed exposure, they estimate the volume of unrecorded transactions and the likely structure of the missing sub‑network.

Overall, the study demonstrates that degree‑based network metrics alone can be misleading when data are incomplete and when firms’ internal attributes drive link formation. The dual disassortative/assortative nature suggests that shocks may propagate quickly within rating clusters even if the global topology appears resilient. Policymakers and risk managers should therefore incorporate firm‑level credit information and exposure metrics when assessing systemic vulnerability. The proposed methodology offers a practical way to reconstruct partially observed financial networks, improving the reliability of contagion models and informing more nuanced regulatory interventions.