The advisory feasibility of Social Network Analysis (SNA) to study social networks have encouraged the law enforcement and security agencies to investigate the terrorist network and its behavior along with key players hidden in the web. The study of the terrorist network, utilizing SNA approach and Graph Theory where the network is visualized as a graph, is termed as Investigative Data Mining or in general Terrorist Network Mining. The SNA defined centrality measures have been successfully incorporated in the destabilization of terrorist network by deterring the dominating role(s) from the network. The destabilizing of the terrorist group involves uncovering of network behavior through the defined hierarchy of algorithms. This paper concerning the destabilization of terrorist network proposes a pioneer algorithm which seems to replace the already available hierarchy of algorithms. This paper also suggests use of the two influential centralities, PageRank Centrality and Katz Centrality, for effectively neutralizing of the network.