Investigation of Key-Player Problem in Terrorist Networks Using Bayes Conditional Probability

  • D. M. Akbar HussainEmail author


In Social Network Analysis (SNA) it is quite conventional to employ graph theory concepts for example cut-points and cut-sets or measuring node centralities like betweenness, degree and closeness to highlight important actors in the network. However, it is also believed that most of these measures alone are inadequate for investigating terrorist/covert networks. In this paper we compute posterior probability using Bayes conditional probability theorem to compute each nodes positional probability to see how probable/likely that the node is a key player. Obviously, larger the probability value higher is the chances that the node is a key actor, the system after words using the computed probability can select an arbitrary number of nodes for elimination to make the network non-functional or severely destroying its capability. We know that that network fragmentation in its simplest form is a count of the number of components, more the number of counts larger is the fragmentation. The reason of calling it simple is because it does not include many aspects of the network for example structure etc. Borgatti has provided a similar measure which does includes the shape and internal structure of the components and high light the important actors in the network. Our computational procedure provides very similar results in highlighting the key player problem. We simulated our computational model through various random networks and we also applied it to the David Krackhardt’s kite network and to 9-11 hijackers network to bench mark our results. It shows that conceptually this framework of evaluation can be used to highlight the key players in terrorist/covert cells.


Social Network Analysis Centrality Measure Betweenness Centrality Geodesic Distance Compute Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Borgatti S. P:. Identifying sets of key players in a network. Computational, Mathematical and Organizational Theory 12(1), pages 21–34, 2006.Google Scholar
  2. 2.
    Borgatti S. P:. The key player problem. In R. Breiger, K. Carley, and P. Pattison, (eds.), Dynamic social network modeling and analysis, workshop summary and papers. National Academy of Sciences Press, pages 241–252, 2003.Google Scholar
  3. 3.
    Borgatti S. P. and M. G. Everett:. The centrality of groups and classes. Journal of Mathematical Sociology 23(3), pages 181–201, 1999.Google Scholar
  4. 4.
    Valdis Krebs:. Connecting the dots, tracking two identified terrorists, 2002.Google Scholar
  5. 5.
    Bavelas A:. A mathematical model for group structures. Human Organization 7, pages 16–30, 1948.Google Scholar
  6. 6.
    Shaw M. E:. Group structure and the behaviour of individuals in small groups. Journal of Psychology 38, pages 139–149, 1954.Google Scholar
  7. 7.
    Bavelas A:. Communication patterns in task oriented groups. Journal of the Acoustical Society of America 22, pages 271–282, 1950.Google Scholar
  8. 8.
    Leavitt Harold J:. Some effects of communication patterns on group performance. Journal of Abnormal and Social Psychology 46, pages 38–50, 1951.Google Scholar
  9. 9.
    Smith Sidney L:. Communication pattern and the adaptability of task-oriented groups: an experimental study. Cambridge, MA, Group networks laboratory, research laboratory of electronics, Massachusetts Institute of Technology, 1950.Google Scholar
  10. 10.
    Bavelas A. and D. Barrett:. An expermental approach to organizational communication. Personnel 27, pages 366–371, 1951.Google Scholar
  11. 11.
    Glanzer M. and R. Glaser:. Techniques for the study of team structure and behaviour. Part II: Empirical studies of the effects of structure. Technical report, Pittsburgh, American Institute, 1957.Google Scholar
  12. 12.
    Glanzer M. and R. Glaser:. Techniques for the study of group structure and behaviour. Part II: Empirical studies of the effects of structure in small groups. Psychological Bulletin 58, pages l–27, 1961.Google Scholar
  13. 13.
    Cohen A. M:. Communication networks in research and training. Personnel Administration 27, pages 18–24, 1964.Google Scholar
  14. 14.
    Shaw M. E:. Communication networks. In L. Berkowitz (ed.), Advances in experimental social psychology, vol. vi, pages 111–147, New York, Academic Press, 1964.Google Scholar
  15. 15.
    Stephenson K. A. and M. Zelen:. Rethinking centrality: methods and examples. Social Networks 11, pages 1–37, 1989.Google Scholar
  16. 16.
    Flament C:. Applications of graph theory to group structure. Englewood Cliffs, NJ, Prentice Hall, 1963.Google Scholar
  17. 17.
    Burgess R. L:. Communication networks and behavioural consequences. Human Relations 22, pages 137–l59, 1968.Google Scholar
  18. 18.
    Snadowski A:. Communication network research: an examination of controversies. Human Relations 25, pages 283–306, 1972.Google Scholar
  19. 19.
    Rogers D. L:. Socio-metric analysis of inter-organizational relations: application of theory and measurement. Rural Socioeonv 39, pages 487–503, 1974.Google Scholar
  20. 20.
    Rogers D. L:. Communication networks in organizations. Communication in organizations, pages 108–148, New York, Free Press, 1976.Google Scholar
  21. 21.
    Cohn B. S. and M. Marriott:. Networks and centres of integration in indian civilization. Journal of Social Research I, pages 1–9, 1958.Google Scholar
  22. 22.
    Pitts F. R:. A graph theoretic approach to historical geography. The Professional Geographer 17, pages 15–20, 1965.Google Scholar
  23. 23.
    Latora V. and M. Marchiori:. A measure of centrality based on network efficiency, preprint cond-mat/0402050, 2004.Google Scholar
  24. 24.
    Freeman Linton C:. A set of measures of centrality based on betweenness. Sociometry 40, pages 35–41, 1971.Google Scholar
  25. 25.
    Freeman Linton C:. Centrality in social networks: conceptual clarification. Social Networks 1, page 215–239, 1979.Google Scholar
  26. 26.
    Anthonisse J. M:. The rush in a graph, University of Amsterdam Mathematical Centre, Amsterdam, 1971.Google Scholar
  27. 27.
    Nieminen J:. On centrality in a graph. Scandinavian Journal of Psychology 15, pages 322–336, 1974.Google Scholar
  28. 28.
    Scott J:. Social networks analysis, 2nd edition, London, Sage Publications, 2003.Google Scholar
  29. 29.
    Sabidussi G:. The centrality index of a graph. Psychometrika 31, pages 581–603, 1966.Google Scholar
  30. 30.
    Shaw M. J., C. Subramaniam, G. W. Tan and M. E. Welge:. Knowledge management and data mining for marketing. Decision Support Systems 31(1), pages 127–137, 2001.Google Scholar
  31. 31.
    Carley K. M., J.-S. Lee and D. Krackhardt:. Destabilizing networks, Dept. of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15143, November 2001.Google Scholar
  32. 32.
    Akbar Hussain D. M:. Destabilization of terrorist networks through argument driven hypothesis model. Journal of Software 2(6), pages 22–29, 2007.Google Scholar
  33. 33.
    Akbar Hussain D. M. and D. Ortiz-Arroy:. Locating key actors in social networks using bayes posterior probability framework, lecture notes in computer science. In Intelligence and Security Informatics, vol. 5376/2008.Google Scholar
  34. 34.
    Ortiz-Arroy D. and D. M. Akbar Hussain:. An information theory approach to identify sets of key players. In Intelligence and Security Informatics, vol. 5376/2008.Google Scholar
  35. 35.
    Adibi J. and J. Shetty:. Discovering important nodes through graph entropy the case of enron email database. In Linkkdd 2005: Proceedings of the 3rd international workshop on link discovery, pages 74–81, ACM, New York, 2005.Google Scholar
  36. 36.
    Freeman L. C., S. P. Borgatti and D. R. White:. Centrality in valued graphs, a measure of betweenness based on network flow. Social Networks 13, pages 141–154, 1991.Google Scholar
  37. 37.
    Newman M. E. J:. A measure of betweenness centrality based on random walks, cond-mat/0309045, 2003.Google Scholar
  38. 38.
    Beauchamp M. A:. An improved index of centrality. Behavioral Science 10, pages 161–163, 1965.Google Scholar
  39. 39.
    Oliver C. Ibe:. Fundamentals of applied probability and random processes, Elsevier Academics Press, ISBN 0-12-088508-5, 2005.Google Scholar
  40. 40.
    Montgomery D. C. and G. C. Runger:. Applied statistics abd probability for engineers, 4th edition, ISBN 978-0-471-74589-1, Wiley, 2006.Google Scholar
  41. 41.
    Koskinen J. H. and T. A. B. Snijders:. Bayesian inference for dynamic social network data. Journal of Statistical Planning and Inference 137, pages 3930–3938, 2007.Google Scholar
  42. 42.
    Siddarth K., H. Daning and C. Hsinchum:. Dynamic social network analysis of a dark network: identifying significant facilitators. In Proceedings of IEEE international conference on intelligence and security informatics, ISI 2007, New Brunswick, NJ, USA, May 23–24, 2007.Google Scholar
  43. 43.
    C. J. Rhodes and E. M. J. Keefe:. Social network topology: a bayesian approach. Journal of the Operational Research Society 58, pages 1605–1611, 2007.Google Scholar
  44. 44.
    Sparrow M.:. The application of netwrok analysis to criminal intelligence: an assessment of the prospects. Social Networks 13, pages 251–274, 1991.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Automation and Control, Department of Electronic SystemsAalborg UniversityEsbjergDenmark

Personalised recommendations