Graph and Network Theory for the analysis of Criminal Networks.

Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the analysis of criminal networks, which are presented in a real-world case study. Starting from available juridical acts, we have extracted data on the interactions among suspects within two Sicilian Mafia clans, obtaining two weighted undirected graphs. Then, we have investigated the roles of these weights on the criminal network's properties, focusing on two key features: weight distribution and shortest path length. We also present an experiment that aims to construct an artificial network that mirrors criminal behaviours. To this end, we have conducted a comparative degree distribution analysis between the real criminal networks, using some of the most popular artificial network models: Watts-Strogatz, Erd\H{o}s-R\'{e}nyi, and Barab\'{a}si-Albert, with some topology variations. This chapter will be a valuable tool for researchers who wish to employ social network analysis within their own area of interest.