International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8 Issue-3, September 2019 1278 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: B2333078219/19©BEIESP DOI:10.35940/ijrte.B2333.098319 Abstract: Social Networks are best represented as complex interconnected graphs. Graph theory analysis can hence be used for insight into various aspects of these complex social networks. Privacy of such networks lately has been challenged and a detailed analysis of such networks is required. This paper applies key graph theory concepts to analyze such social networks. Moreover, it also discusses applications and proposal of a novel algorithm to analyze and gather key information from terrorist social networks. Investigative Data Mining is used for this which is defined as when Social Network Analysis (SNA) is applied to Terrorist Networks to gather useful insights about the network.. Index Terms: Graph Theory, Graph Mining, Investigative Data Mining, Social Network Analysis. I. INTRODUCTION A graph typically is a collection of non-linear nodes connected using edges. A social network can typically be defined using a graph, where the members of the network comprise of the nodes and their mutual connections are represented using the edges. Social network analysis is a key technique in present day human communication analysis. It has also gained a significant popularity in anthropology, biology, communication studies, economics, geography, information studies, organizational studies and human psychology and has become a popular topic of speculation and study. Humans have used the thought of social systems freely for over a century to mean complex arrangements of connections between individuals from social frameworks by any stretch of the imagination scales, from interpersonal to worldwide. Graph theory involves analysis of graphs and extracting useful information and represents it using standard metrics such as degree, etc. Graph representation of SNA topologies are used for various purposes such as community detection, network structures, random walks and temporal networks. Social network analysis as mentioned has been useful in numerous fields and much of its impact is shared in [1] and [2]. There have been numerous issues with these ever so important social networks. A good compilation of these issues can be found [5] here. Revised Manuscript Received on September 15, 2019 Krishna Ganeriwal*, SCOPE, VIT University, Vellore, India. Email: ganeriwalk@gmail.com Gayathri P, SCOPE, VIT University, Vellore, India. Email: pgayathri@vit.ac.in G. Gopichand, SCOPE, VIT University, Vellore, India. Email: gopichand.g@vit.ac.in H Santhi, SCOPE, VIT University, Vellore, India. Email: hsanthi@vit.ac.in In this paper, we discuss various metrics that can be applied to social network graphs such as centrality, closeness, betweenness, bridge, clustering coefficient, page-rank centrality, etc. Furthermore, the existing algorithms and their disadvantages are also analyzed and finally, a novel algorithm is proposed to counter some of these disadvantages. In the closing section of the paper potential areas for future research is discussed. II. GRAPH METRICS IN SNA Typically social networks can be considered as unweighted and undirected graphs for analysis and investigative purposes. In these graphs the users represent nodes and the connection between these users is illustrated using edges between the concerned nodes. The resulting graph can be mathematically formulated as an adjacency matrix (M ij ) in the following format: M ij = This representation of the social network enables easy calculation and representation of metrics and network structure, mainly clustering coefficient, mixing time, efficiency of the network, Eigen vectors and degree. Following is an insight into these metrics and their use in SNA: A. Metrics SNA Metrics is regarded as among one of the broadest researches in graphical representation of Social network analysis. By knowing relations between various nodes inside a network, we can compute useful information about networks and essentially they can reveal network structures. Having metrics additionally implies we can gather essential information about the system and utilize the information for a few purposes. 1. Centrality: Centrality gives key insight into the importance of a node in a particular network and has been well explained by the work of Freeman [3]. There are a few basic types of centrality measures used, which are: a. Degree centrality: Provides information on how well connected a node is in a given network and is represented using: b. Betweenness: Provides numerical data on the extent to which a node intermediates the Data Mining in Social Networks and its Application in Counterterrorism Krishna Ganeriwal, Gayathri P, G. Gopichand, H. Santhi