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

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.

[1]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[2]  Wang Jiaxin,et al.  Investigative Data Mining: Identifying Key Nodes in Terrorist Networks , 2006, 2006 IEEE International Multitopic Conference.

[3]  Stefan Thurner,et al.  Introduction to the Theory of Complex Systems , 2018, Oxford Scholarship Online.

[4]  Kathleen M. Carley,et al.  A complex networks approach to find latent clusters of terrorist groups , 2019, Appl. Netw. Sci..

[5]  Bisharat Rasool Memon.  Identifying Important Nodes in Weighted Covert Networks Using Generalized Centrality Measures , 2012, 2012 European Intelligence and Security Informatics Conference.

[6]  Michael Aizenman.  Ergodic Theory in Statistical Mechanics. , 1975 .

[7]  Carlo Morselli,et al.  Assessing Vulnerable and Strategic Positions in a Criminal Network , 2010 .

[8]  Mohsen Kalantari,et al.  A New Methodological Framework for Crime Spatial Analysis Using Local Entropy Map , 2016 .

[9]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[10]  Eric D. Kolaczyk,et al.  Modeling and Prediction for Processes on Network Graphs , 2020, Statistical Analysis of Network Data with R.

[11]  Ernesto Estrada,et al.  The Structure of Complex Networks: Theory and Applications , 2011 .

[12]  Pasquale De Meo,et al.  Detecting criminal organizations in mobile phone networks , 2014, Expert Syst. Appl..

[13]  Thomas M. Cover,et al.  Probability and Information. , 1986 .

[14]  Douglas J. Klein,et al.  Centrality measure in graphs , 2010 .

[15]  Dirk Helbing,et al.  Saving Human Lives: What Complexity Science and Information Systems can Contribute , 2014, Journal of statistical physics.

[16]  Klaus Nordhausen,et al.  Statistical Analysis of Network Data with R , 2015 .

[17]  António M. Lopes,et al.  Analysis of global terrorism dynamics by means of entropy and state space portrait , 2016 .

[18]  Nancy Rodríguez.  Recent advances in mathematical criminology: comment on "Statistical physics of crime: a review" by M.R. D'Orsogna and M. Perc. , 2015, Physics of life reviews.

[19]  Edward Ott,et al.  Characterizing the dynamical importance of network nodes and links. , 2006, Physical review letters.

[20]  J. A. Rodríguez,et al.  Functional centrality in graphs , 2006, math/0610141.

[21]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[22]  Malcolm K. Sparrow,et al.  The application of network analysis to criminal intelligence: An assessment of the prospects , 1991 .

[23]  Hanning Yuan,et al.  Identifying influential nodes of global terrorism network: A comparison for skeleton network extraction , 2020 .

[24]  Pasquale De Meo,et al.  Network Structure and Resilience of Mafia Syndicates , 2015, Inf. Sci..

[25]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[26]  Paolo Campana,et al.  Centrality, Mobility, and Specialization: A Study of Drug Markets in a Non-metropolitan Area in the United Kingdom , 2020 .

[27]  E. Chaisson.  Cosmic Evolution: The Rise of Complexity in Nature , 2001 .

[28]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[29]  Edoardo M. Airoldi,et al.  Getting Started in Probabilistic Graphical Models , 2007, PLoS Comput. Biol..

[30]  C. Tsallis,et al.  Nonextensive Entropy: Interdisciplinary Applications , 2004 .

[31]  Matjaz Perc,et al.  Statistical physics of crime: A review , 2014, Physics of life reviews.

[32]  Guido Caldarelli,et al.  Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science , 2007 .

[33]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[34]  Mikko Kivelä,et al.  Generalizations of the clustering coefficient to weighted complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data with R , 2020, Use R!.

[36]  Tao Wen,et al.  Measuring the complexity of complex network by Tsallis entropy , 2019, Physica A: Statistical Mechanics and its Applications.

[37]  Xin Du,et al.  Key Node Ranking in Complex Networks: A Novel Entropy and Mutual Information-Based Approach , 2019, Entropy.

[38]  Eric D. Kolaczyk,et al.  Descriptive Analysis of Network Graph Characteristics , 2014 .

[39]  Bruno Requião da Cunha,et al.  Topology, robustness, and structural controllability of the Brazilian Federal Police criminal intelligence network , 2018, Applied Network Science.

[40]  Hui Li,et al.  Centrality analysis of online social network big data , 2018, 2018 IEEE 3rd International Conference on Big Data Analysis (ICBDA).

[41]  Dosam Hwang,et al.  A Model for Predicting Terrorist Network Lethality and Cohesiveness , 2020, IEA/AIE.

[42]  Crime as a complex system: comment on "Statistical physics of crime: a review" by M.R. D'Orsogna and M. Perc. , 2015, Physics of life reviews.

[43]  Eric D. Kolaczyk,et al.  Network Topology Inference , 2014 .

[44]  Tobun Dorbin Ng,et al.  Terrorism and Crime Related Weblog Social Network: Link, Content Analysis and Information Visualization , 2007, 2007 IEEE Intelligence and Security Informatics.

[45]  Artur Ziviani,et al.  Network anomaly detection using nonextensive entropy , 2007, IEEE Communications Letters.

[46]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[47]  Jenny Chalmers,et al.  Social network analysis of Australian poly-drug trafficking networks: How do drug traffickers manage multiple illicit drugs? , 2017, Soc. Networks.

[48]  Stanislas Dehaene,et al.  An accumulator model for spontaneous neural activity prior to self-initiated movement , 2012, Proceedings of the National Academy of Sciences.

[49]  Tao Ren,et al.  Multi-Type Node Detection in Network Communities , 2019, Entropy.

[50]  Eric D. Kolaczyk,et al.  Mathematical Models for Network Graphs , 2020, Use R!.

[51]  Sebastiano Vigna,et al.  Axioms for Centrality , 2013, Internet Math..

[52]  Matjaž Perc,et al.  Physics for better human societies: reply to comments on "Statistical physics of crime: a review". , 2015, Physics of life reviews.

[53]  Alexander Gutfraind,et al.  A graph database framework for covert network analysis: An application to the Islamic State network in Europe , 2017, Soc. Networks.

[54]  Faraz Zaidi,et al.  Communities and hierarchical structures in dynamic social networks: analysis and visualization , 2011, Social Network Analysis and Mining.

[55]  Joshua D. Freilich,et al.  Changing organizational structures of jihadist networks in the Netherlands , 2017, Soc. Networks.