Criminal networks arise from the unique attempt to balance a need of establishing frequent ties among affiliates to facilitate the coordination of illegal activities, with the necessity to sparsify the overall connectivity architecture to hide from law enforcement. This efficiency-security tradeoff is also combined with the creation of groups of redundant criminals that exhibit similar connectivity patterns, thus guaranteeing resilient network architectures. State-of-the-art models for such data are not designed to infer these unique structures. In contrast to such solutions we develop a computationally-tractable Bayesian zero-inflated Poisson stochastic block model (ZIP-SBM), which identifies groups of redundant criminals with similar connectivity patterns, and infers both overt and covert block interactions within and across such groups. This is accomplished by modeling weighted ties (corresponding to counts of interactions among pairs of criminals) via zero-inflated Poisson distributions with block-specific parameters that quantify complex patterns in the excess of zero ties in each block (security) relative to the distribution of the observed weighted ties within that block (efficiency). The performance of ZIP-SBM is illustrated in simulations and in a study of summits co-attendances in a complex Mafia organization, where we unveil efficiency-security structures adopted by the criminal organization that were hidden to previous analyses.

翻译：犯罪网络的形成源于一种独特的平衡尝试：既需在成员间建立频繁联系以协调非法活动，又必须稀疏化整体连接结构以躲避执法。这种效率与安全的权衡还伴随着冗余犯罪群体的形成——这些群体展现出相似的连接模式，从而保证网络的弹性架构。现有针对此类数据的先进模型并非为推断此类独特结构而设计。与此类解决方案不同，我们开发了一种计算可行的贝叶斯零膨胀泊松随机块模型（ZIP-SBM），该模型能识别具有相似连接模式的冗余犯罪群体，并推断这些群体内部及群体间公开与隐蔽的区块交互。这是通过以下方式实现的：采用具有区块特定参数的零膨胀泊松分布对加权联系（对应犯罪成对间的互动次数）进行建模，这些参数量化了每个区块内零联系超额量（安全性）相对于该区块内观测到的加权联系分布（效率）的复杂模式。ZIP-SBM的性能通过模拟实验以及对一个复杂黑手党组织中峰会共同出席情况的研究得到验证，其中我们揭示了该犯罪组织采用但先前分析未能发现的效率-安全结构。