International Journal of Computer Applications (0975 – 8887) International Conference on Microelectronics, Circuits and Systems (MICRO-2014) 34 Modeling of Social Network using Graph Theoretical Approach Sweata Mishra School of computing sciene Kziranga University Assam,India Rupam Borboruah School of computing science Kaziranga University Assam,India Sandip Rakshit School of computing science Kaziranga University Assam,India Bharadwaj choudhury School of computing science Kaziranga University Assam,India ABSTRACT This paper describes the model of formation and properties of social network via a graph theoretical approach. The paper considers the interaction between different sets of people in a social network. It also describes the additional information about each individual in a network. We have also described the matrix representation of social network. The purpose of this paper is to review the graphical model of social networking. This paper is about how two persons are related to each other and how they can access each other‟s resources. A social network is a social structure made up of individuals (or organizations) called "nodes", which are tied(connected) by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige. Keywords Cut vertex and cut edge, graph metric, adjacency matrix, Social graph topology 1. INTRODUCTION Social network is a" group of internet-based application, that is build on the ideological and technological foundation of web, and allow the creation and exchange of user generated content"[10]. Understanding such a network provides us useful insights of ways regarding how social communities are formed and interactions thereafter. Therefore it is required to generate a graphical view in order to understand the network, so that refinement or analysis in future is easier. Social network is the structure, which shows the relations between individuals and organization. It indicates the ways in which they are connected through various social familiarities ranging from casual acquaintance to close familiar bonds [1] In this paper, we have shown the mapping of relationship between individuals and organizations. We have represented it using graph G(V,E) which is a collection of vertices and edges. Vertices are the people and groups and edges are relationships between them. Most important part of modeling a social network is their sub models, through which we can get more information about connections between two different vertices i.e. individuals or communities. 2. SOCIAL GRAPH TOPOLOGY Social network can be represented as undirected graph G(V,E) where V is the set of vertices representing users and E is the set of edges representing social ties such as friendship, kinship and the likes. Graphs are used to represent communication networks or social networks and the analysis of some of their basic properties can help on evaluating and improving the performance of networking solution.[2] 3. NODE DEGREE In a graph, the degree of a vertex is denoted by deg(v) is the number of edges incident in that vertex. Since in a graph G(V,E) , vertex represents the user and edge represents the relationship or friendship , a user‟s degree represents the number of friend a user can have or the pages he likes. A page may belong to any organization, communities etc. Understanding the degree of a node gives the overall idea of how many social acquaintances an individual is having. A „like‟ in a social network typically involves information sharing. Different studies have shown that increase in the number of participants results in a weak link on privacy of users [3], [4], [5]. 4. SOCIAL MODEL The reason behind using graphical model in social network is to describe the network more elaborately and systematically. Using graphical model allows us to describe the properties of network elaborately and distinctly. The relation between individuals can be mapped using graphical method and how one can access the resource of other user(s) can be described. There is a big issue of privacy while using social network, as it contains huge amount of sensitive data. 4.1 Modeling: Let us consider two friends A and B. If we want to model the relation between them we can simply draw the graph below. We have used undirected graph to show the relation as A and B both can share each other resources. The reason for using undirected graph is that an edge from one friend to another always means that the access of resource is on both the direction.