# Social Network Consists Of Group Computer Science Essay

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This chapter presents the overview of social network analysis. Presenting its applications, advantages and disadvantages also describe graphs in social network. The structure of this chapter is as follows: Section 2.2 describes social network background. Then section 2.3 deals with Graph in Social Network. Links in social networks is discussed in section 2.4.Section 2.5 describes Small world hypothesis. Section 2.6 deals with application of social network. Finally the chapter ends with summary and discussion is reported in section 2.7.

## Introduction

Online network systems have become popular in many social, biological and information system in recent year. Much research has been done in social network, which is increasingly growing and form a large complex network. Social network such as facebook provides a platform for users to share their interest, photos & post etc with their friend. A social network can be well described by a network graph, in which node represents users and edges between nodes represent some association. In most social network links are dynamics and change over the time in network [2]. Analysis of such a network is challenging task because of it huge and dynamic behaviour where number of social networks can also be constructed from specific kinds of interactions in different communities. A classical example would be the scientific community in which bibliographic networks can be constructed from either co-authorship or citation data. These are all novel forms of social networks, each of which brings with it a set of unique challenges for the purpose of analysis.

## Social Network

A social network consists of a group of people and connections between them. These connections can be any type of social link that implies a relationship between two people. There is an existing field of mathematics called graph theory that deals with any structure, like a social network, that can be represented by nodes and edges. The discipline of graph theory has been extended by researchers into the field of social network analysis. There are two types of social network analysis dynamic analysis and static analysis [2]. In static network analysis network changes over due course of time and analysis is done in particular time duration. On the other hand dynamic network varies at very large rate over time. Analysis of such a network is challenging. Many temporal characteristic of the network can be determined through the dynamically change behaviour of the network. Such large interconnectivity in social network link prediction provides recommendation for users on the basis of their common interest. Instant messaging network is an example of such dynamic network, also link prediction has been applied in the analysis where prediction of collaboration in co authorship network, or relationship between underground terrorist, where link prediction has to be fast and accurate.

## Graph in Social Network

Figure 2.1 : Social Network Graph G.

A better way to understand the structure of a social network is to view it as graph G (V, E) where V is the set of nodes and E is the set of edges. The nodes represent the user and the edge or link represents the association or interaction between the nodes of a social network. Let us consider a graph G shown in Figure 2.1, with 12 nodes i.e. V {n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12} and 16 edges i.e. E {(n1, n2), (n1, n3), (n1, n4)â€¦}. Graph G is an undirected graph representing a friendship or collaboration network.

## Path

A path in the network graph G (V, E) is a finite sequence of the form n5-n6-n7-n9 having a node visited at most once. A path does not have any circuit or there are no repeated nodes [3].

## Path Length

Total number of edge in a path is the path length of any node pair in graph G. for example a 3 length path is represented with 4 nodes and 3 edges as shown in graph G having path between node (n5, n9) is n5-n6-n7-n9 [3].

## Matrix Representation of Graph

A graph can be represented as an adjacency matrix of n x n, the entries of matrix shows the edge between the nodes (ni, nj). The label of rows and columns of matrix represents the nodes of the graph and corresponding entries between nodes represent the edge if the nodes are connected [4].

Figure 2.2 : Adjacency Matrix A of graph G

We can represent a graph G by an adjacency matrix; if there are n = |V | vertices v1, v2â€¦. vn, this is an n x n array whose (i, j)th entry is

For undirected graphs, the matrix is symmetric since an edge {u, v} can be taken in either direction.

An adjacency matrix is filled with 0 or 1, where 0 represents the nodes is not connected and 1 shows that the nodes are connected. A network graph G is represented by an adjacency matrix A of dimension 12 x 12 shown in Figure 2.2. Matrix A is a symmetric matrix for an undirected graph.

## Graph Traversal Algorithm

Graph traversal algorithms are used to visit all the nodes in a graph and the widely used algorithms for this purpose are depth-first search and breadth-first search [3].

## Depth First Search

Depth First Search (DFS) [3][4] is graph traversal algorithm that traverses the graph to search the node at the target depth or to traverse the entire node in a graph. DFS expands the source node of the graph and goes in depth until the desire depth is not reaches or up to the last node that has no children. After reaching the target depth the searches backtracks and return to the recent node that is pushed into the stack top and start the search from that node as shown in figure 2.4. DFS is the basis for many graph-related algorithms. Application area of DFS differs the space-time analysis, theoretically DFS is used to traversed the whole graph which takes time O(|V| + |E|) and space O(|V|) in worst case to store the visited node and the current search node in stack. For example consider a graph shown in Figure 2.3, DFS start from node d and revel all the path

## Figure 2.3 : Graph for DFS example

Considering the starting node 'd' in a graph shown in Figure 3, DFS uses stack for the track of path to be visited and an array for identifying the visited node. The stack representation of graph shown in Figure 2.3 is shown in Figure 2.4 and the corresponding graph of ordered visted node is shown in Figure 2.5.

Figure 2.4 : DFS Stack

## Figure 2.5 : DFS Traverse Node Graph

## Advantage of DFS

Memory requirement of depth first search is less as compared to breadth first search, In depth first search a linear space of memory is needed for the search graph because the algorithm store the node in stack from root node to current node where as in breadth first search each level of node is saved to reach the next level.DFS has O(bd) time complexity up to the depth d where b is branching factor. It is a time limited search which generate same set of nodes as BFS, but the generation order of nodes in both algorithm is different. If we consider a limited depth graph for DFS then it will find a node or a targeted solution in very less time and require less space.

## Disadvantage of DFS

DFS may suffer from non-termination as the length of path is infinite because the graph that has to be search is too large to visit all the nodes in it. Solution for this problem is to predefine the depth to some value d as to search a target node, the algorithm fail if the predefine value is less than d. There is no guarantee that the DFS reaches desired solution.

## Links in Social Network

Examples of a relationship between people studied in social network analysis include friendship, we can record only those of which we have evidence having collaboration with authors, or belonging to the same social area [5]. In other disciplines nodes and links can be used to represent towns and highways, computers and cabling, or companies and ownership. Considering a co authorship collaboration in which an author may connect with more than one author as shown in graph g in Figure 2.6, the formation of new link between yellow node which is present in the previous state of graph g' shown in Figure 2.7. For instance an author may publish an article with other authors and connects the node with a direct link. To illustrate this, consider that all we know about an author A is their article in collaboration with other co author B and C. then for this graph V = {A,B,C,D,E} and E = {{A,B},{A,C},{D,C}...}as shown in figure 2.6 and 2.7. A sociogram represents a complex system - a human society, or at least part of it. Social networks are representations of complexity, they are neither totally ordered lattices, nor random distributions of nodes and links, but rather have special properties of their own.

## Summary and Discussion

In recent years, online social networking systems has emerged as a latest tread in data mining, where users interact with each other to share content such as photos etc. Online social networks such as Facebook.com, MySpace.com, Hi5.com, etc. contain gigabytes of data that can be mined to make predictions about who is a friend of whom. Online social networks gather information on users' social contacts, construct a large interconnected social network, and recommend other people to users based on their common friends. Online social networks recommend new friends to registered users based on local-based features of the graph (i.e. based on the number of common friends that two users share). Social networks are highly dynamic objects; they grow and change quickly over time through the addition of new edges, signifying the appearance of new interactions in the underlying social structure. Online social network plays an important role in link prediction and structuring these as graph is seen to be implemented efficiently over the years.