# The Whole Is Greater than the Sum of the Parts: A Multilayer Approach on Criminal Networks +
## 4 Discussion  
In this paper, we used a real criminal dataset related to an anti-mafia operation known as Montagna, which was concluded in 2007. Parsing a two hundred-page pre-trial detection order by the Court of Messina, we initially built three simple graphs, one for meetings, one for phone calls and one for crimes committed together by the suspected criminals. Some suspects who met and called each other also committed crimes together. Therefore, we identified meetings, phone calls and crimes as layers of a multiplex network. For this reason, we created a weighted and undirected multilayer network, where edge weights represented the number of meetings, phone calls or crimes. We initially studied the three layers of the Montagna multiplex network separately applying some descriptive measures that are typical of SNA such as the number of connected components, the size of the largest connected component, the density, the average clustering coefficient, the average path length and the diameter. Then, we used actor measures from the multilayer network analysis to study the degree of the 20 most central actors, their degree deviation, their neighborhood and exclusive neighborhood, and their relevance and exclusive relevance. These measures are useful to understand the importance of an actor with respect to the whole network and on each specific layer. Finally, we used layer measures from multilayer network analysis to study the overlapping of actors and links, the correlation among the actor degree on each layer and the dissimilarity among the degree distributions on each layer. Our experiments show how traditional measures, which are usually used for simple graphs, such as the Jaccard or Pearson correlation coefficients, allow obtaining significant results even on multilayer networks. Thus, the generalization of traditional network science measures sounds promising for the study of multilayer networks. The study of correlation among the layers of a multilayer network, and therefore the study of the overlapping of actors and edges in it, allows us to understand if each layer contains unique information. The lack of overlapping among edges proves that compared with the study of the single layers, the analysis of multiple layers within a criminal network provides a more nuanced understanding of its structure and of the strategic position of actors in it. Figure 4: Degree distributions of the three layers—Meetings, Phone Calls and Crimes—where \(p_{k}\) provides the probability that a randomly selected node in each layer has degree \(k\). A key actor in a certain layer may not be central in any aother layer nor for the multilayer network. The identification of key actors in a criminal network may be of particular salience for law enforcement efforts to reduce the capabilities of a criminal network. LEAs could consider key actors across different layers to make decisions regarding targets for surveillance, intelligence and arrest. For this reason, LEAs should collect multiplex data including data on different types of edges across a criminal network [13]. Analyzing multiplex data, we could also redefine the concept of criminal. The level of criminality of a specific actor could be quantified based on his connections among the layers. Multiplex data could also be useful to face the missing data problem in criminal networks, which are usually incomplete, incorrect and inconsistent [25]. LEAs may have limited resources or make unintentional errors. Some individuals unrelated to the criminal organization such as relatives, friends or other frequent contacts may appear during the investigations. Moreover, some members of the criminal organization try to avoid detection using intermediaries, coding messages or by refraining from the use of the telephone. In criminal network analysis, missing data can refer to missing nodes and/or missing edges.