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# Final social network_analysis

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Paper emphasizes on how are social networks managed and used for Business. This paper was Presented in an International Conference in Pune

Paper emphasizes on how are social networks managed and used for Business. This paper was Presented in an International Conference in Pune

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• 4. Figure 1: Area wise presence of Social Network services
• 5. 2. GRAPH THEORY AND ITS APPLICATIONS IN SOCIAL NETWORK ANALYSISGraph Theory is one of the youngest branches of Mathematics. It is used in various fields likeOperations research, Social network analysis, Economics, Electrical networks, Power grids etc.Fundamental concept of graph theory lies in graphs. Graphs have main entity as nodes (vertices)and edges (links) that link the various nodes. A graph is usually denoted as G= (V, E). Vcorresponds to sets of vertices and E corresponds to set of Edges. Generally the numbers ofvertices are denoted as &#x2018;n&#x2019; and edges denoted as &#x2018;m&#x2019;.Vertices are also referred to as Nodes and in Social networks they are referred to as actors. Anedge corresponds to ties in Social networks. They depict the type of relationship between twonodes.For example: In Facebook when we add someone as a friend, we get a window stating that howyou know that person (Friend, colleague, never met etc). If the person to whom I sent a request ismy colleague, a relationship is formed between two nodes in the social graph as shown belowfigure. Graph 1: Linking between two nodes (as represented in social network).Node 1 had sent request to the Node 2 to add him in its friends list. When we perform Socialnetwork analysis, the graph will contain only those nodes that are connected to each other withsome relationship.If node a had sent a request to node b to add him as a friend and node b did not accept therequest, then there wont be any relationship between node a and node b. So this sub graph won&#x2019;tbe shown in analysis of either of them. 2.1 Some basic concepts in graphs and their application in Social Network analysis:
• 6. Graph 2: Reference graph 2.1.1 ADJACENCY MATRIXVertices Vi and Vj are said to be adjacent if a link (i, j) exists between them. In the above graph 2Node a and Node b, Node c and Node d, Node d and Nod e etc are adjacent.Every graph can be associated with an adjacency matrix. Adjacency matrix is nxn matrix. In thisaij = aji = 1 if the vertex vi and vj are adjacent and aij = aji = 0 if vertex vi and vj are notadjacent. a b c d e f 0 1 0 0 0 0 a 1 0 1 0 0 0 b 0 1 0 1 1 0 c 0 0 1 0 1 0 d 0 0 0 1 0 1 e 0 0 0 0 1 0 fTable 3: Adjacency Matrix
• 7. The adjacent matrix is used to determine relationships. A complex network graph can be brokendown to a matrix for simple understanding. If every vertex is connected to every other vertexthen the graph is called complete graph. This is used to find strong relationships between actorsin Social network analysis.Adjacent matrix is used to find density of graph. Density can be defined as the level ofcompleteness of graph. Density is determined by dividing number of edges or links in the graphwith the maximum number possible. In our reference graph, the density is 5/15 = 0.3333.Density is used to determine the nature of a Social graph. 2.1.2 CONNECTEDNESSAnother important property of graph is Connectedness. It is defined as the ability to reach fromany one of the vertex of the graph to any other vertex of the graph. Graphs with this property arecalled connected. The graph 2 is connected graph since we can reach from any vertex to thegraph to any other vertex. Connectedness is used to determine the size of network.For example: In Facebook it will help us to determine whether we can be linked to the personwho is linked to your friend. 3. ANALYSIS OF SOCIAL NETWORK SERVICESSocial Network Analysis (SNA) is basically the study of relationships between individuals orbetween individual and community or relationship within a group. It includes the analysis ofsocial structures to reveal informal connections between them. The relationship betweenindividuals is often represented in form of network. This network can be studied using Networktheory. A network can be represented in form of a graph. A graph has nodes and edges.Similarly, in a social network individuals are represented as nodes and their relationship isrepresented in form of edges or links. There can be various kinds of relationship or ties betweenindividual actors such as friends, colleagues, neighbor, school mates etc.Social network analysis aims to explore some of the following tasks: 3.1 CENTRALITYCentrality aims to fine the most important actor in the network. In a Social network, centralitywill try to find the person to which maximum of the nodes are connected in a particular networkgraph.
• 8. Graph 3: Network explaining centralityThe above network has 10 actors, that is nodes represented by circles. Node1, node2, node3,node4 and node5 fall into one network and node6, node7, node8, node9 and node10 fall inseparate network. The two networks are connected by a common node that is node 3. Here wecan state that the node 3 is the most important or central node. 3.2 COMMUNITIESVarious actors in a Social network who shares common interests come together and form acommunity. A community can be of the people who support Manchester united football team orpeople who like to red Sidney Sheldon books. In this task we identify these communities bystudying network topology. 3.3 TYPE OF RELATIONSHIPThe Links between the two nodes in a Social network are of different types. Two nodesrepresenting two persons can be linked together as Friends, colleagues, school &#x2013;mates, projectpartners etc. In this task of SNA we identify the different types on links of an individual node toother nodes in network.
• 9. Figure 2: Shows various types of relationshipsHere when a node wants to be connected to other node (Richard). We can define the type ofrelationship between the two nodes. Above are the types of relationships in Facebook. 3.4 NETWORK MODELINGHere in this task we try to model or simulate a real world network using simple mechanisms suchas graphs. We try to capture all the patterns present in the network on to the model. 3.5 ANALYZING STRONG AND WEAK TIESEvery node in network graph is related or linked to some other node. The linking is call tiebetween the nodes. A tie can be strong or weak. 3.5.1 STRONG TIES A strong tie defines the two individuals to be actively tied to each other. Both share manycommon interests and spend ample amount of time with each other. In a nutshell they are closefriends. For example: On Facebook, John and Rick are strongly tied if they have many common interestsand friend of John is probably friend of Rick. That is they share many common friends. In thefigure 4, node1, node2, node3, node4 and node5 are strongly tied to each other. Node1 isconnected to node2 and node3. And also node2 and node3 are friends of each other. The nodes ina strong tie are more socially involved with each other. Ties can also lead to predict certainrelationship in a network. For example: If a node A has edges to nodes B and C, then the B-Cedge is especially likely to form if A&#x2019;s edges to B and C are both strong ties. 3.5.2 WEAK TIESA tie between two nodes is said to be weak tie if two nodes are the given nodes are less sociallyinvolved with each other. They belong to a community that shares common interest. But theydon&#x2019;t have many common friends. Also they do not share many common interests.
• 10. Graph 4: Strong and Weak TiesThe type of tie between Node4 and Node6 is a weak tie. This is because they share very fewcommon interests and friends. Let&#x2019;s assume Node4 and Node6 represents two people who live insame street. They do not have any other common interests and friends. They are not very sociallyinvolved with each other. We can term the weak tie as low density network and strong tie as highdensity network. As stated by Mark Granovetter, weak ties are very important part of a socialnetwork.Here in the above diagram, Node4 and Node6 are weakly tied to each other. But Node4 andNode6 have their own dense networks. Thus a weak tie between Node4 and Node6 has led thetwo networks merge together. Through this weak tie the nodes belonging to community1 (grey)can be linked to the community (blue). In absence of this weak tie the two networks would neverhave merged. 3.5.3 BENEFITS OF WEAK TIESThe research in the past 3 decades shows that the weak ties are beneficial for a number ofoutcomes. Weak ties also lead to knowledge development, sub-group consolidation. They alsoplay important role in organizing larger groups that are formed by weak ties among the nodesthat have their own small primary networks.Weak ties prove to be an important tool in Social Network analysis. Analyzing a large networkthat has millions of individuals and thousands of communities is very complex. So we can breaka particular community in to sub groups on the basis of weak ties. In the figure below if we wantto break up the complex network to a smaller one, we can identify the weaker ties and thenseparate the two sub groups in the network and make the network easy for analysis.
• 11. Graph 5: Elimination of weak ties leads to formation of two sub-groups 4. ANALYSIS OF A FACEBOOK PROFILEThe practical applications of the above concepts can be shown in an example, wherein aFacebook account is analyzed. While analyzing, we always consider a profile from which theanalysis starts. Analyzing can be done using tools available from Internet, along with someinternal factors that can be seen from the profile from the person.The analysis will result in determining strong ties and weak. A tie will be considered as strong ifboth the nodes share many common interest and they frequently post on each other&#x2019;s wall andmost important is that they should have many friends in common. On the basis of these criteriawe can determine the strong ties in the graph 6 profile.
• 12. Graph 6: Graph of analysis of a Facebook profile
• 13. STRENGTH NUMBER OF MUTUAL OF TIE NAME FRIENDS (RANK) Tarvinder Singh 72 1 Deepak Kuniyal 41 2 Sukhjinder singh Aujla 27 3 Gurvinder Singh Aujla 20 4 Sapna Nair 24 5 Evie Satheesan 27 6 Kuldeep Katiyar 21 7 Jaswinder Singh Randhawa 11 8 Amol Patil 19 9 Vicky D&#x2019;souza 17 10 Ronita D&#x2019;costa 22 11 Kamini Darji 19 12 Supriya Auti 23 13 Vikrant Dhore 19 14 Gurvinder Singh padda 14 15 Rohit Dahiya 22 16 Pawan Sandhu 14 17 Bilal Mulla 12 18 Saurabh Aluwalia 20 19 Anand Rai 19 20 Sushant Satam 16 21 Sarita Balakrishnan 18 22 Ajay Sharma 19 23 Komal Kumar 19 24Table 4: List of related nodes with regards to strength of Tie.The above profile belongs to the Tarvinder Singh. The person named Deepak kuniyal has 41common friends, also almost all friends of Tarvinder are friend of Deepak also. Also if weobserve carefully, Jaswinder Singh Randhawa has only 11 mutual friends but has rank 8. It isbecause the strength of a tie is not only determined by number of mutual friend but also withregards to the activity of the friend. A participant may have less mutual friend but is very activethat is he continuously posts on the others wall and share comments. Such participant may getbetter rank than the others with same number of mutual friends.Cluster can be a group of participants interested in particular activity or a group of friends whoare densely linked to each other. A social graph also helps in identifying the clusters. Clustersalso help in identifying the reach ability and from one node to the other. Participants with samecolor that are isolated from the their cluster are the non active members of the group.
• 14. Graph 7: Determination of clusters from Social graph. 5. BUSINESS APPLICATIONS OF SOCIAL NETWORK ANALYSISCOMMUNICATIONSocial network analysis of an organization helps to determine the communication flow andknowledge flow with in the organization. It can also detect and help to rectify the flaws in the
• 15. communication system. For Example: - Social network analysis in an organization determinedthat an employee &#x2018;A&#x2019; does not have good ties with his senior &#x2018;B&#x2019; and so he does not effectivelycommunicate with &#x2018;B&#x2019; instead he communicates with &#x2018;C&#x2019; who is the head of other department.FUNCTIONINGSocial network analysis can determine the inter relation and functioning of various departmentswithin an organization.TEAM BUILDING OR GROUP FORMATIONSNA can help in formation of teams. SNA determines the efficiency of informal communicationwithin a group. According the people with better bonding can be grouped together to make astrong operational team.Example of Social Network Analysis of a small organization of 5 actors:Column1 JOHN JANE AMELI ROSE DEBORAHJOHN 0 0 0 1 1JANE 0 0 0 1 0AMELI 0 1 0 1 0ROSE 0 0 0 0 1 DEBORAH 0 0 1 0 0Table 5: Communications Hierarchy of an organization revealed by SNAHere the above names are the employees of an organization. The table shows that John alwaysgoes to Rose or Deborah for any information about the sales of a product. Jane consults Rose andAmeli consults Jane and Rose. Rose consults Deborah and Deborah consults Ameli for anyinformation. Here thus Ameli is basically the indirect or direct source of information for all theemployees. After this information the organization can hire more people to assist Ameli so thather work pressure is reduced.Thus the above table also shows that the most influential person in the organization is Rose, whois consulted by three people (John, Jane and Ameli).
• 16. 6. CONCLUSIONGraphs provide visualization for almost everything. In this article we have tried to focus on theon the Social network and analysis of Social networks using Graph theory. Since 2008 thenumber of people on Social nets has increased considerably. The analysis of such networks givesus information about the behavior of a group and identifies informal relationships among people.Social network analysis in an organization can facilitate proper functioning of variousdepartments, so as to minimize the friction between them. SNA can also help HR department ofan organization to streamline the team formation process and optimize the operations.Applications of SNA for organizational analysis are called ONA (Organizational networkanalysis). ONA is upcoming field and growing very fast in the recent scenario. ACKNOWLEDGEMENTOur deepest thanks to Professor Sudipto Chakraborty for his precious guidance in writing thisdocument. He has gone through the article and put lot of efforts to correct document whenneeded.
• 17. REFERENCES1. Vincenzo Cosenza, world map of Social Networks, December 2010.2. Robin Wauters, It&#x2019;s a Facebook World, 13 June 2011 WWW.techcrunch.com3. Boyd danah. &#x201C;Social Network Sites: Public, Private, or What?&#x201D; Knowledge Tree 13 May 2007.4. Monica Chew, Dirk Balfanz and Ben Laurie &#x201C;Under mining Privacy in social Networks&#x201D;.5. Stephen P. Borgatti, Graph Theory.6. Lei Thang and Huan Liu, Graph Mining application to Social network analysis.7. B. Carolan and G. Natriello, Strong Ties, weak Ties: Relational Dimensions of Learning settings.8. Kate Ehrlich and Inga Carboni, Inside Social Networks.9. Borgatti, S.P., Bernard, H.R., and Pelto, P. 1992. NSF Summer Institute on Ethnographic Research Methods. Available from Analytic Technologies www.analytictech.com.10. Borgatti, S. and Foster, P. (2003). The network paradigm in organizational research: A review and typology. Journal of Management 29(6), 991-1013.11. www.wikipedia.com