Criminal Networks Analysis in Missing Data scenarios through Graph Distances

Data collected in criminal investigations may suffer from: (i) incompleteness, due to the covert nature of criminal organisations; (ii) incorrectness, caused by either unintentional data collection errors and intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times, or in different formats. In this paper we analyse nine real criminal networks of different nature (i.e., Mafia networks, criminal street gangs and terrorist organizations) in order to quantify the impact of incomplete data and to determine which network type is most affected by it. The networks are firstly pruned following two specific methods: (i) random edges removal, simulating the scenario in which the Law Enforcement Agencies (LEAs) fail to intercept some calls, or to spot sporadic meetings among suspects; (ii) nodes removal, that catches the hypothesis in which some suspects cannot be intercepted or investigated. Finally we compute spectral (i.e., Adjacency, Laplacian and Normalised Laplacian Spectral Distances) and matrix (i.e., Root Euclidean Distance) distances between the complete and pruned networks, which we compare using statistical analysis. Our investigation identified two main features: first, the overall understanding of the criminal networks remains high even with incomplete data on criminal interactions (i.e., 10% removed edges); second, removing even a small fraction of suspects not investigated (i.e., 2% removed nodes) may lead to significant misinterpretation of the overall network.