A CONCEPTUAL STUDY OF SOCIAL NETWORK AND ITS ANALYSIS USING GRAPH THEORY Mr. Tarvinder Singh Analyst Directi Internet Solutions Pvt Ltd Ms. Sneha Joshi Research Associate Cheers Interactive Pvt Ltd ABSTRACTSocial Networking websites are ubiquitous and large numbers of teenagers spend their time onthese web sites accessing public life. Social networking websites allow their users to developtheir digital profile and keep in touch with their friends and involve themselves in multi-userapplications. Due to large number of users and reach, SNS’s has attracted the attention of manyindustry and academic researchers. In this article we study various aspects of the SNS and try topropose a most precise definition of the same. Visualization always plays and important role inunderstanding in depth architecture of any system. The analysis of SNS can be visualized usingthe fundamental concepts of Graph theory. Social Network Analysis views the relationships inthe SNS with reference to Network Theory (Graph Theory) consisting of Nodes and Edges orLinks and tries to extract the information that gives us the better understanding of SocialNetwork. Graph theory in Social Network Analysis (SNA) describes the users or actors as Nodesand their relationship as edges that connect them. This article will primarily emphasize on theanalysis of the Social networks. This article brings together various social and technicaldynamics of the SNS’s. 1. INTRODUCTION 1.1 HISTORY OF SOCIAL NETWORKSThe history of Social Networks can be traced back to the year 1968, when JCR Licklider andRobert W. Taylor wrote an Essay titled “The computer as a Communication device” and statedthat, to communicate with someone you will not send a letter or a telegram – you will simplyidentify the people whose files should be linked to yours”. Many efforts were made in the earlydays to support and built Social networks via computer mediated communication. These effortsresulted in systems such as Usenet, ARPANET (Advanced Research Projects Agency Network,which was the first operational packet switching network), LISTSERV etc. These systems werevery first foundation for Social networks. After the World Wide Web (WWW) was created in1991 by Tim Berners Lee and Robert Calliau, the concept of online community advanced furtherin the form of services like Tripod (Founded by Bo Peabody and Brett Hershey, 1992) andGeocities (Founded by Bohnett and John Rezner, 1994). These services enabled the users to setup their own personal homepage that can be linked to the home pages of other members. Thesewere the very first instances of Digital profiles of users on Internet.The first instance of Social networking website was www.classmates.com. Classmate enabledpeople to find the school friends with their Names. The first complete Social networking website
was PlanetAll. PlanetAll had more than 100000 groups. Users can link themselves to theirfriends by a common link such as the University (where they studied together) or Organization(where they worked together).From 2002 onwards many Social networking sites came into existence like Friendster, Myspace,Facebook, Twitter, Hi5 etc. These sites were able to bag a huge numbers of users in very shorttime. 1.2 SOCIAL NETWORK SITESA social network service uses software to build online social networks for people or communitiesof people who share common interests and activities or who are interested in exploring theinterests and activities of others. There are about 250 Social network sites that has total of about850 Million users. The total numbers of Internet users are about 1750 Million. The statisticsdepict that every second user on the Internet is a user of a at least one Social network service.The percentage increase every year in numbers of users of Social network Service is about 25%.Most of the Social network services are web-based. They provide number of ways (Chat, IM,discussion, Blog etc) for users to interact with each other.Once a user is logged in Social network site he/she is asked to create a digital profile. Theprofiles resemble their own personality and illustrate how they see themselves. Participants canuse text, images, videos, favorite books and hobbies to create their profile. The profiles of theparticipants can linked together through “friend list”. “Friend-list” can be a group or communityof people who share common interests. This is referred to as close ties. The number of Friends inthe list is the people whom the participant has made its potential audience with whom he canshare pictures, audios, videos and make or receive comments on certain actions.Other important feature of the Social network service is the “The Wall” and “Testimonials”.Wall is the private page of a participant on which other participants who has access to the profileof the participant can comment. Profiles, Friends and comments are the core elements of thestructure of Social network service.Following figure indicates the percentage increase in number of users of Social network servicesworld-wide.Social Networking Growth by Worldwide RegionJune 2008 vs. June 2007Total Worldwide Audience, Age 15+ - Home and Work LocationsSource: ComScore World Metrix Unique Visitors (000) Jun-07 Jun-08 Percent ChangeWorldwide 464,437 580,510 25%Asia Pacific 162,738 200,555 23%Europe 122,527 165,256 35%North America 120,848 131,255 9%
Latin America 40,098 53,248 33%Middle East - Africa 18,226 30,197 66%Table 1: Area wise increase in the users of Social network services.The Above table shows that the Social network has picked up very fast in the Middle-east regionthe year 2007 to 2008. The overall increase was 25%Worldwide Growth among Selected Social Networking SitesJune 2008 vs. June 2007Total Worldwide Audience, Age 15+ Home and Work LocationsSource: comScore World Metrix Total Unique Visitors (000) Jun-2007 Jun-2008 % ChangeTotal Internet : Total Audience 778,310 860,514 11%Social Networking 464,437 580,510 25%FACEBOOK.COM 52,167 132,105 153%MYSPACE.COM 114,147 117,582 3%HI5.COM 28,174 56,367 100%FRIENDSTER.COM 24,675 37,080 50%ORKUT.COM 24,120 34,028 41%BEBO.COM 18,200 24,017 32%SKYROCK NETWORK 17,638 21,041 19%Table 2: Percentage increase in the users of Top Social network services.Among all the top social network sites, Face book has attracted highest number of users in theyear 2007-2008. During the period of 2007-2009 Facebook has the highest growth in Asiancountries and Middle-East.In 2011 Facebook alone has about 600 Million users. Leading Social network service in Indiawas Orkut till the year 2009. In June 2011 it was found that Facebook has highest number ofusers in India.What makes Facebook different from other leading Social network services? The answer isexplained in the Danah Boyd’s research. She mentioned that Facebook is meant for kids that area part of hegemonic society. That is they go to college, give importance to studies, and lots more.Also Facebook is also attracts many elder people. On the other hand she mentioned that many ofthe Social network services like Myspace and Hi5 have majority (80%) of the participants thatare a part of a band or they are not much educated. MySpace has most of the kids who aresocially ostracized at school because they are geeks, freaks, or queers.Following Figure shows the geographic locations throughout the globe where Facebook andother Social network services have their presence.
Figure 1: Area wise presence of Social Network services
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 ‘n’ and edges denoted as ‘m’.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’tbe shown in analysis of either of them. 2.1 Some basic concepts in graphs and their application in Social Network analysis:
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
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.
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 –mates, projectpartners etc. In this task of SNA we identify the different types on links of an individual node toother nodes in network.
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’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’t have many common friends. Also they do not share many common interests.
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’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.
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’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.
Graph 6: Graph of analysis of a Facebook profile
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’souza 17 10 Ronita D’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.
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
communication system. For Example: - Social network analysis in an organization determinedthat an employee ‘A’ does not have good ties with his senior ‘B’ and so he does not effectivelycommunicate with ‘B’ instead he communicates with ‘C’ 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).
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.
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