Structural asymmetry as a fraud signature: detecting collusion with Heron's Information Coefficient

Abstract: Fraud in public procurement remains a persistent challenge, especially in large, decentralized systems like Brazil's Unified Health System. We introduce Heron's Information Coefficient (HIC), a geometric measure that quantifies how subgraphs deviate from the global structure of a network. Applied to over eight years of Brazilian bidding data for medical supplies, this measure highlights collusive patterns that standard indicators may overlook. Unlike conventional robustness metrics, the Heron coefficient focuses on the interaction between active and inactive subgraphs, revealing structural shifts that may signal coordinated behavior, such as cartel formation. Synthetic experiments support these findings, demonstrating strong detection performance across varying corruption intensities and network sizes. While our results do not replace legal or economic analyses, they offer an effective complementary tool for auditors and policymakers to monitor procurement integrity more effectively. This study demonstrates that simple geometric insight can reveal hidden dynamics in real-world networks better than other Information Theoretic metrics.