Abstract
Understanding and inferring connectivity patterns within illicit networks is an important task facing criminologists. Criminal organised networks operate under a fundamental tension: maintaining enough regular interactions to coordinate operations effectively while simultaneously sparsifying their network architecture to evade law enforcement detection. Although this efficiency-security trade-off is a recognised concept in criminology, existing statistical approaches lack the capacity to accurately model and infer these underlying structural patterns. To address this limitation, we developed a tractable Bayesian network model, the zero-inflated Poisson stochastic block model (ZIP–SBM), which simultaneously identifies groups or blocks of redundant criminals having similar connectivity patterns, and infers both overt and covert block interactions within and across these groups. In particular, a key feature of this model is that it facilitates the discovery of connectivity ties between criminals that would otherwise remain hidden. The utility of the ZIP–SBM approach is demonstrated through numerical simulations and an empirical application, which motivated this project, analysing summit co-attendances within a complex Mafia organization, revealing structural efficiency-security trade-offs that remained undetected in prior investigations.
Reference: Chaoyi Lu, Daniele Durante, Nial Friel (2026). Zero-inflated stochastic block modelling of efficiency-security trade-offs in weighted criminal networks, Journal of the Royal Statistical Society Series A: Statistics in Society. https://doi.org/10.1093/jrsssa/qnaf029