Using Mathematical Models in Decision Making Methodologies to Find Key Nodes in the Noordin Dark Network

William P. Fox, Sean F. Everton

Department of Defense Analysis, Naval Postgraduate School, Monterey, USA.

DOI: 10.4236/ajor.2014.44025                

Abstract

A Dark Network is a network that cannot be accessed through tradition means. Once uncovered, to any degree, dark network analysis can be accomplished using the SNA software. The output of SNA software includes many measures and metrics. For each of these measures and metric, the output in ORA additionally provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning best methods to disrupt or deceive a given dark network. In the Noordin Dark network, different nodes were identified as key nodes based upon the metric used. Our goal in this paper is to use methodologies to identify the key players or nodes in a Dark Network in a similar manner as we previously proposed in social networks. We apply two multi-attribute decision making methods, a hybrid AHP & TOPSIS and an average weighted ranks scheme, to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We compare these methods by illustration using the Noordin Dark Network with seventy-nine nodes. We discuss sensitivity analysis that is applied to the criteria weights in order to measure the change in the ranking of the nodes.

Keywords

Social Network Analysis, Multi-Attribute Decision Making, Analytical Hierarchy Process (AHP), Decision Criterion, Weighted Criterion, TOPSIS, Node Influence, Sensitivity Analysis, Average Weighted Ranks

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Everton, S. and Roberts, N. (2011) Strategies for Combating Dark Networks. Journal of Social Structure, 12, 1-32.
[2]	Milward, H.B. and Raab, J. (2003) Dark Networks as Problems. Journal of Public Administration Research and Theory, 13, 413-439. http://dx.doi.org/10.1093/jopart/mug029
[3]	Milward, H.B. and Raab, J. (2003) Dark Networks as Problems. Paper Presented to the 8th Public Management Research Conference at the School of Policy, Planning and Development at University of Southern California, Los Angeles, 29 September-1 October 2005.
[4]	Newman, M. (2010) Networks: An Introduction. Oxford University Press, Oxford. http://dx.doi.org/10.1093/acprof:oso/9780199206650.001.0001
[5]	Carley, K. (2001-2011) Organizational Risk Analyzer (ORA). Carnegie Mellon University, Center for Computational Analysis of Social and Organizational Systems (CASOS), Pittsburgh.
[6]	Everton, S. (2012) Disrupting Dark Networks. Cambridge University Press, Cambridge, UK and New York, USA. http://dx.doi.org/10.1017/CBO9781139136877
[7]	Fox, W. and Everton, S. (2014) Using Data Envelopment Analysis and the Analytical Hierarchy Process to Find Node Influences in a Social Network. Journal of Defense Modeling and Simulation, 11, 1-9.
[8]	Fox, W. and Everton, S. (2013) Mathematical Modeling in Social Network Analysis: Using TOPSIS to Find Node Influences in a Social Network. Journal of Mathematics and System Science, 3, 531-541.
[9]	Fox, W. (2102) Mathematical Modeling of the Analytical Hierarchy Process Using Discrete Dynamical Systems in Decision Analysis. Computers in Education Journal, 22, 27-34.
[10]	Giordano, F., Fox, W. and Horton, S. (2103) A First Course in Mathematical Modeling. 5th Edition, Brooks-Cole Publishers, Boston.
[11]	Burden, R. and Faires, D. (2011) Numerical Analysis. 9th Edition, Brooks-Cole Publishers, Boston.
[12]	Huang, I., Keisler, J. and Linkov, I. (2011) Multi-Criteria Decision Analysis in Environmental Science: Ten Years of Applications and Trends. Science of the Total Environment, 409, 3578-3594. http://dx.doi.org/10.1016/j.scitotenv.2011.06.022
[13]	Hwang, C. and Yoon, K. (1981) Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag Publishers, New York. http://dx.doi.org/10.1007/978-3-642-48318-9
[14]	Hwang, C., Lai, Y. and Liu, T. (1993) A New Approach for Multiple Objective Decision Making. Computers and Operational Research, 20, 889-899. http://dx.doi.org/10.1016/0305-0548(93)90109-V
[15]	Yoon, K. (1987) A Reconciliation among Discrete Compromise Situations. Journal of Operational Research Society, 38, 277-286. http://dx.doi.org/10.1057/jors.1987.44
[16]	Satty, T. (1980) The Analytical Hierarchy Process. McGraw Hill, New York.
[17]	Alinzhad, A. and Amini, A. (2011) Sensitivity Analysis of TOPSIS Technique: The Results of Change in the Weight of One Attribute on the Final Ranking of Alternatives. Journal of Optimization in Industrial Engineering, 7, 23-28.