Abstract
Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or 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 analyze 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 using two specific methods: (i) random edge removal, simulating the scenario in which the Law Enforcement Agencies fail to intercept some calls, or to spot sporadic meetings among suspects; (ii) node removal, modeling the situation in which some suspects cannot be intercepted or investigated. Finally we compute spectral distances (i.e., Adjacency, Laplacian and normalized Laplacian Spectral Distances) and matrix distances (i.e., Root Euclidean Distance) between the complete and pruned networks, which we compare using statistical analysis. Our investigation identifies two main features: first, the overall understanding of the criminal networks remains high even with incomplete data on criminal interactions (i.e., when 10% of edges are removed); second, removing even a small fraction of suspects not investigated (i.e., 2% of nodes are removed) may lead to significant misinterpretation of the overall network.
Highlights
Criminal organizations can be defined as groups operating outside the boundaries of the law, that profit from providing illicit goods and services in public demand in an illicit manner, and for which achievements come at the detriment of other individuals, groups or societies [1]
DA displays a saturation effect that makes the results difficult to be interpreted. This distance is not effective for highlighting the effects of missing data on criminal networks. From this metric it might seem that the two pruned networks of Philippines Kidnappers (PK) and Summits Network (SN) show a greater deviation from their original counterparts, but this is due to the inner structure of this metric, which is highly influenced by the node degree
In this paper we analyzed nine datasets of real criminal networks extracted from six police operations to investigate the effects of missing data
Summary
Criminal organizations can be defined as groups operating outside the boundaries of the law, that profit from providing illicit goods and services in public demand in an illicit manner, and for which achievements come at the detriment of other individuals, groups or societies [1]. A network (or graph) G = hN, Ei consists of two finite sets N and E [30]. . ., n} contains the nodes (or vertices, actors), and n is the size of the network, while the set E N × N contains the edges (or links, ties) between the nodes. A network is called undirected if all its edges are bidirectional. If the edges are defined by ordered pairs of nodes, the network is called directed.
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