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Entropy and Network Centralities as Intelligent Tools for the Investigation of Terrorist Organizations - PubMed

  • ️Fri Jan 01 2021

Entropy and Network Centralities as Intelligent Tools for the Investigation of Terrorist Organizations

Alexandros Z Spyropoulos et al. Entropy (Basel). 2021.

Abstract

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.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1

The network of “Jamaah Islamiah section of Indonesia”.

Figure 2
Figure 2

The overall protagonists of the “Jamaah Islamiah section of Indonesia”. The protagonists are represented as larger oranges spheres. Most nodes have degree >0.3, but the node 177 (0.7) stands out. Most nodes have low values (<0.2) as mediators, but the 0177 (0.3) stands out. Most nodes are team players (clustering >0.6), but the nodes 177 (1), 577 (1), 800 (1), 1504 (1), 1507 (1) and 1509 (1) stand out as team players.

Figure 3
Figure 3

The evolution of normalized entropies. A peak of the entropies appears in 2004. The entropies increase from 1995 to 2004, but the entropy of clustering increases shakenly after 2002. All entropies decrease after 2004, the entropy of betweenness decreases a little faster.

Figure 4
Figure 4

The network of “Hamburg Cell”.

Figure 5
Figure 5

The overall protagonists of the “Hamburg Cell”. The protagonists are represented as larger light blue spheres. Most nodes have degree >0.3, but the nodes 64 (0.5), 61 (0.4) and 60 (0.4) stand out. Most nodes have low values (<0.1) as mediators, but the 1016 (0.2) stands out. Most nodes are not team players (clustering =0), but the nodes 58 (0.7), 1032 (0.7), 1012 (0.6) and 57 (0.4) stand out as team players.

Figure 6
Figure 6

The evolution of normalized entropies. Two peaks appear in 1996 and 1998. All entropies decrease after 2001. The entropy of betweenness decreases faster. A plateau of high entropies appears in the period 1998 to 2001.

Figure 7
Figure 7

The network of the “al-Qaeda section of Madrid”.

Figure 8
Figure 8

The overall protagonists of the “al-Qaeda section of Madrid”. The protagonists are represented as larger light blue spheres. Most nodes have degree >0.2, but the nodes 3132 (0.3), 3144 (0.3) and 3157 (0.3) stand out. Most nodes have low values (<0.1) as mediators, but the 3134 (0.2) stands out. All nodes are not team players (clustering =0).

Figure 9
Figure 9

The evolution of normalized entropies. A sharp peak appears in 2003. All entropies decrease after 2003. The entropy of betweenness decreases faster.

Figure 10
Figure 10

The network of the “Jamaah Islamiah section of Philippines”.

Figure 11
Figure 11

The overall protagonists of the “Jamaah Islamiah section of Philippines”. The protagonists are represented as larger pink spheres. Most nodes have high degree (≥0.7), but the 153 (0.9) and 163 (0.8) stand out. Most nodes have low values (≤0.1) as mediators but the nodes 193 (0.3) and 163 (0.2) stand out. Most nodes are team players (clustering ≥0.4), but the node 163 (1) stands out as team player.

Figure 12
Figure 12

The evolution of normalized entropies. There is a high plateau of the values of entropies from 2000 to 2001. Afterwards, all entropies decrease for the next two years, and then, they increase to some extend after 2005. The entropy of betweenness decreases faster.

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