In recent years, law enforcement authorities have increasingly used mathematical tools to support criminal investigations, such as those related to terrorism. In this work, two relevant questions are discussed: "How can the different roles of members of a terrorist organization be recognized?" and "are there early signs of impending terrorist acts?" These questions are addressed using the tools of entropy and network theory, more specifically centralities (degree, betweenness, clustering) and their entropies. These tools were applied to data (physical contacts) of four real terrorist networks from different countries. The different roles of the members are clearly recognized from the values of the selected centralities. An early sign of impending terrorist acts is the evolutionary pattern of the values of the entropies of the selected centralities. These results have been confirmed in all four terrorist networks. The conclusion is expected to be useful to law enforcement authorities to identify the roles of the members of terrorist organizations as the members with high centrality and to anticipate when a terrorist attack is imminent, by observing the evolution of the entropies of the centralities.
Keywords: centralities measures; criminal investigations; entropy in crime investigation; network roles identification; police investigations; terrorist networks; weighted network.