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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
                                         ABSTRACT

Social Networking websites are ubiquitous and large numbers of teenagers spend their time on
these web sites accessing public life. Social networking websites allow their users to develop
their digital profile and keep in touch with their friends and involve themselves in multi-user
applications. Due to large number of users and reach, SNS’s has attracted the attention of many
industry and academic researchers. In this article we study various aspects of the SNS and try to
propose a most precise definition of the same. Visualization always plays and important role in
understanding in depth architecture of any system. The analysis of SNS can be visualized using
the fundamental concepts of Graph theory. Social Network Analysis views the relationships in
the SNS with reference to Network Theory (Graph Theory) consisting of Nodes and Edges or
Links and tries to extract the information that gives us the better understanding of Social
Network. Graph theory in Social Network Analysis (SNA) describes the users or actors as Nodes
and their relationship as edges that connect them. This article will primarily emphasize on the
analysis of the Social networks. This article brings together various social and technical
dynamics of the SNS’s.

                                1. INTRODUCTION
                        1.1 HISTORY OF SOCIAL NETWORKS

The history of Social Networks can be traced back to the year 1968, when JCR Licklider and
Robert W. Taylor wrote an Essay titled “The computer as a Communication device” and stated
that, to communicate with someone you will not send a letter or a telegram – you will simply
identify the people whose files should be linked to yours”. Many efforts were made in the early
days to support and built Social networks via computer mediated communication. These efforts
resulted in systems such as Usenet, ARPANET (Advanced Research Projects Agency Network,
which was the first operational packet switching network), LISTSERV etc. These systems were
very first foundation for Social networks. After the World Wide Web (WWW) was created in
1991 by Tim Berners Lee and Robert Calliau, the concept of online community advanced further
in the form of services like Tripod (Founded by Bo Peabody and Brett Hershey, 1992) and
Geocities (Founded by Bohnett and John Rezner, 1994). These services enabled the users to set
up their own personal homepage that can be linked to the home pages of other members. These
were the very first instances of Digital profiles of users on Internet.

The first instance of Social networking website was www.classmates.com. Classmate enabled
people 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 their
friends 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 short
time.
                            1.2 SOCIAL NETWORK SITES

A social network service uses software to build online social networks for people or communities
of people who share common interests and activities or who are interested in exploring the
interests and activities of others. There are about 250 Social network sites that has total of about
850 Million users. The total numbers of Internet users are about 1750 Million. The statistics
depict 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. The
profiles resemble their own personality and illustrate how they see themselves. Participants can
use text, images, videos, favorite books and hobbies to create their profile. The profiles of the
participants can linked together through “friend list”. “Friend-list” can be a group or community
of people who share common interests. This is referred to as close ties. The number of Friends in
the list is the people whom the participant has made its potential audience with whom he can
share 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 profile
of the participant can comment. Profiles, Friends and comments are the core elements of the
structure of Social network service.

Following figure indicates the percentage increase in number of users of Social network services
world-wide.

Social Networking Growth by Worldwide Region
June 2008 vs. June 2007
Total Worldwide Audience, Age 15+ - Home and Work Locations
Source: ComScore World Metrix
                                Unique Visitors (000)
                                Jun-07       Jun-08          Percent Change
Worldwide                       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 region
the year 2007 to 2008. The overall increase was 25%

Worldwide Growth among Selected Social Networking Sites
June 2008 vs. June 2007
Total Worldwide Audience, Age 15+ Home and Work Locations
Source: comScore World Metrix
                                 Total Unique Visitors (000)
                                 Jun-2007      Jun-2008       % Change
Total 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 the
year 2007-2008. During the period of 2007-2009 Facebook has the highest growth in Asian
countries and Middle-East.

In 2011 Facebook alone has about 600 Million users. Leading Social network service in India
was Orkut till the year 2009. In June 2011 it was found that Facebook has highest number of
users in India.

What makes Facebook different from other leading Social network services? The answer is
explained in the Danah Boyd’s research. She mentioned that Facebook is meant for kids that are
a 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 of
the Social network services like Myspace and Hi5 have majority (80%) of the participants that
are a part of a band or they are not much educated. MySpace has most of the kids who are
socially ostracized at school because they are geeks, freaks, or queers.

Following Figure shows the geographic locations throughout the globe where Facebook and
other Social network services have their presence.
Figure 1: Area wise presence of Social Network services
2. GRAPH THEORY AND ITS APPLICATIONS IN SOCIAL NETWORK ANALYSIS

Graph Theory is one of the youngest branches of Mathematics. It is used in various fields like
Operations 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). V
corresponds to sets of vertices and E corresponds to set of Edges. Generally the numbers of
vertices 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. An
edge corresponds to ties in Social networks. They depict the type of relationship between two
nodes.
For example: In Facebook when we add someone as a friend, we get a window stating that how
you know that person (Friend, colleague, never met etc). If the person to whom I sent a request is
my colleague, a relationship is formed between two nodes in the social graph as shown below
figure.




       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 Social
network analysis, the graph will contain only those nodes that are connected to each other with
some relationship.
If node a had sent a request to node b to add him as a friend and node b did not accept the
request, then there wont be any relationship between node a and node b. So this sub graph won’t
be 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 MATRIX

Vertices Vi and Vj are said to be adjacent if a link (i, j) exists between them. In the above graph 2
Node 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 this
aij = aji = 1 if the vertex vi and vj are adjacent and aij = aji = 0 if vertex vi and vj are not
adjacent.
                       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
             f


Table 3: Adjacency Matrix
The adjacent matrix is used to determine relationships. A complex network graph can be broken
down to a matrix for simple understanding. If every vertex is connected to every other vertex
then the graph is called complete graph. This is used to find strong relationships between actors
in Social network analysis.
Adjacent matrix is used to find density of graph. Density can be defined as the level of
completeness of graph. Density is determined by dividing number of edges or links in the graph
with 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 CONNECTEDNESS

Another important property of graph is Connectedness. It is defined as the ability to reach from
any one of the vertex of the graph to any other vertex of the graph. Graphs with this property are
called connected. The graph 2 is connected graph since we can reach from any vertex to the
graph 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 person
who is linked to your friend.

                  3. ANALYSIS OF SOCIAL NETWORK SERVICES

Social Network Analysis (SNA) is basically the study of relationships between individuals or
between individual and community or relationship within a group. It includes the analysis of
social structures to reveal informal connections between them. The relationship between
individuals is often represented in form of network. This network can be studied using Network
theory. 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 is
represented in form of edges or links. There can be various kinds of relationship or ties between
individual actors such as friends, colleagues, neighbor, school mates etc.

Social network analysis aims to explore some of the following tasks:

                                     3.1 CENTRALITY

Centrality aims to fine the most important actor in the network. In a Social network, centrality
will try to find the person to which maximum of the nodes are connected in a particular network
graph.
Graph 3: Network explaining centrality

The 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 in
separate network. The two networks are connected by a common node that is node 3. Here we
can state that the node 3 is the most important or central node.

                                          3.2 COMMUNITIES

Various actors in a Social network who shares common interests come together and form a
community. A community can be of the people who support Manchester united football team or
people who like to red Sidney Sheldon books. In this task we identify these communities by
studying network topology.

                                3.3 TYPE OF RELATIONSHIP

The Links between the two nodes in a Social network are of different types. Two nodes
representing two persons can be linked together as Friends, colleagues, school –mates, project
partners etc. In this task of SNA we identify the different types on links of an individual node to
other nodes in network.
Figure 2: Shows various types of relationships

Here when a node wants to be connected to other node (Richard). We can define the type of
relationship between the two nodes. Above are the types of relationships in Facebook.

                                 3.4 NETWORK MODELING

Here in this task we try to model or simulate a real world network using simple mechanisms such
as graphs. We try to capture all the patterns present in the network on to the model.

                       3.5 ANALYZING STRONG AND WEAK TIES

Every node in network graph is related or linked to some other node. The linking is call tie
between 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 many
common interests and spend ample amount of time with each other. In a nutshell they are close
friends.
 For example: On Facebook, John and Rick are strongly tied if they have many common interests
and friend of John is probably friend of Rick. That is they share many common friends. In the
figure 4, node1, node2, node3, node4 and node5 are strongly tied to each other. Node1 is
connected to node2 and node3. And also node2 and node3 are friends of each other. The nodes in
a strong tie are more socially involved with each other. Ties can also lead to predict certain
relationship in a network. For example: If a node A has edges to nodes B and C, then the B-C
edge is especially likely to form if A’s edges to B and C are both strong ties.

                                       3.5.2 WEAK TIES

A tie between two nodes is said to be weak tie if two nodes are the given nodes are less socially
involved with each other. They belong to a community that shares common interest. But they
don’t have many common friends. Also they do not share many common interests.
Graph 4: Strong and Weak Ties

The type of tie between Node4 and Node6 is a weak tie. This is because they share very few
common interests and friends. Let’s assume Node4 and Node6 represents two people who live in
same street. They do not have any other common interests and friends. They are not very socially
involved with each other. We can term the weak tie as low density network and strong tie as high
density network. As stated by Mark Granovetter, weak ties are very important part of a social
network.
Here in the above diagram, Node4 and Node6 are weakly tied to each other. But Node4 and
Node6 have their own dense networks. Thus a weak tie between Node4 and Node6 has led the
two 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 never
have merged.

                              3.5.3 BENEFITS OF WEAK TIES

The research in the past 3 decades shows that the weak ties are beneficial for a number of
outcomes. Weak ties also lead to knowledge development, sub-group consolidation. They also
play important role in organizing larger groups that are formed by weak ties among the nodes
that have their own small primary networks.
Weak ties prove to be an important tool in Social Network analysis. Analyzing a large network
that has millions of individuals and thousands of communities is very complex. So we can break
a particular community in to sub groups on the basis of weak ties. In the figure below if we want
to break up the complex network to a smaller one, we can identify the weaker ties and then
separate 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 PROFILE

The practical applications of the above concepts can be shown in an example, wherein a
Facebook account is analyzed. While analyzing, we always consider a profile from which the
analysis starts. Analyzing can be done using tools available from Internet, along with some
internal 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 if
both the nodes share many common interest and they frequently post on each other’s wall and
most important is that they should have many friends in common. On the basis of these criteria
we 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               24
Table 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 41
common friends, also almost all friends of Tarvinder are friend of Deepak also. Also if we
observe carefully, Jaswinder Singh Randhawa has only 11 mutual friends but has rank 8. It is
because the strength of a tie is not only determined by number of mutual friend but also with
regards to the activity of the friend. A participant may have less mutual friend but is very active
that is he continuously posts on the others wall and share comments. Such participant may get
better 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 who
are densely linked to each other. A social graph also helps in identifying the clusters. Clusters
also help in identifying the reach ability and from one node to the other. Participants with same
color 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 ANALYSIS

COMMUNICATION
Social network analysis of an organization helps to determine the communication flow and
knowledge 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 determined
that an employee ‘A’ does not have good ties with his senior ‘B’ and so he does not effectively
communicate with ‘B’ instead he communicates with ‘C’ who is the head of other department.

FUNCTIONING
Social network analysis can determine the inter relation and functioning of various departments
within an organization.

TEAM BUILDING OR GROUP FORMATION
SNA can help in formation of teams. SNA determines the efficiency of informal communication
within a group. According the people with better bonding can be grouped together to make a
strong operational team.

Example of Social Network Analysis of a small organization of 5 actors:

Column1            JOHN            JANE           AMELI          ROSE           DEBORAH
JOHN                           0              0              0              1                     1
JANE                           0              0              0              1                     0
AMELI                          0              1              0              1                     0
ROSE                           0              0              0              0                     1
 DEBORAH                    0             0              1                  0                     0
Table 5: Communications Hierarchy of an organization revealed by SNA

Here the above names are the employees of an organization. The table shows that John always
goes to Rose or Deborah for any information about the sales of a product. Jane consults Rose and
Ameli consults Jane and Rose. Rose consults Deborah and Deborah consults Ameli for any
information. Here thus Ameli is basically the indirect or direct source of information for all the
employees. After this information the organization can hire more people to assist Ameli so that
her work pressure is reduced.

Thus the above table also shows that the most influential person in the organization is Rose, who
is consulted by three people (John, Jane and Ameli).
6. CONCLUSION

Graphs provide visualization for almost everything. In this article we have tried to focus on the
on the Social network and analysis of Social networks using Graph theory. Since 2008 the
number of people on Social nets has increased considerably. The analysis of such networks gives
us information about the behavior of a group and identifies informal relationships among people.
Social network analysis in an organization can facilitate proper functioning of various
departments, so as to minimize the friction between them. SNA can also help HR department of
an organization to streamline the team formation process and optimize the operations.
Applications of SNA for organizational analysis are called ONA (Organizational network
analysis). ONA is upcoming field and growing very fast in the recent scenario.

                                  ACKNOWLEDGEMENT

Our deepest thanks to Professor Sudipto Chakraborty for his precious guidance in writing this
document. He has gone through the article and put lot of efforts to correct document when
needed.
REFERENCES

1. Vincenzo Cosenza, world map of Social Networks, December 2010.
2. Robin Wauters, It’s a Facebook World, 13 June 2011 WWW.techcrunch.com
3. Boyd danah. “Social Network Sites: Public, Private, or What?”
    Knowledge Tree 13 May 2007.
4. Monica Chew, Dirk Balfanz and Ben Laurie “Under mining Privacy in social Networks”.
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

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Final social network_analysis

  • 1. 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 ABSTRACT Social Networking websites are ubiquitous and large numbers of teenagers spend their time on these web sites accessing public life. Social networking websites allow their users to develop their digital profile and keep in touch with their friends and involve themselves in multi-user applications. Due to large number of users and reach, SNS’s has attracted the attention of many industry and academic researchers. In this article we study various aspects of the SNS and try to propose a most precise definition of the same. Visualization always plays and important role in understanding in depth architecture of any system. The analysis of SNS can be visualized using the fundamental concepts of Graph theory. Social Network Analysis views the relationships in the SNS with reference to Network Theory (Graph Theory) consisting of Nodes and Edges or Links and tries to extract the information that gives us the better understanding of Social Network. Graph theory in Social Network Analysis (SNA) describes the users or actors as Nodes and their relationship as edges that connect them. This article will primarily emphasize on the analysis of the Social networks. This article brings together various social and technical dynamics of the SNS’s. 1. INTRODUCTION 1.1 HISTORY OF SOCIAL NETWORKS The history of Social Networks can be traced back to the year 1968, when JCR Licklider and Robert W. Taylor wrote an Essay titled “The computer as a Communication device” and stated that, to communicate with someone you will not send a letter or a telegram – you will simply identify the people whose files should be linked to yours”. Many efforts were made in the early days to support and built Social networks via computer mediated communication. These efforts resulted in systems such as Usenet, ARPANET (Advanced Research Projects Agency Network, which was the first operational packet switching network), LISTSERV etc. These systems were very first foundation for Social networks. After the World Wide Web (WWW) was created in 1991 by Tim Berners Lee and Robert Calliau, the concept of online community advanced further in the form of services like Tripod (Founded by Bo Peabody and Brett Hershey, 1992) and Geocities (Founded by Bohnett and John Rezner, 1994). These services enabled the users to set up their own personal homepage that can be linked to the home pages of other members. These were the very first instances of Digital profiles of users on Internet. The first instance of Social networking website was www.classmates.com. Classmate enabled people to find the school friends with their Names. The first complete Social networking website
  • 2. was PlanetAll. PlanetAll had more than 100000 groups. Users can link themselves to their friends 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 short time. 1.2 SOCIAL NETWORK SITES A social network service uses software to build online social networks for people or communities of people who share common interests and activities or who are interested in exploring the interests and activities of others. There are about 250 Social network sites that has total of about 850 Million users. The total numbers of Internet users are about 1750 Million. The statistics depict 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. The profiles resemble their own personality and illustrate how they see themselves. Participants can use text, images, videos, favorite books and hobbies to create their profile. The profiles of the participants can linked together through “friend list”. “Friend-list” can be a group or community of people who share common interests. This is referred to as close ties. The number of Friends in the list is the people whom the participant has made its potential audience with whom he can share 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 profile of the participant can comment. Profiles, Friends and comments are the core elements of the structure of Social network service. Following figure indicates the percentage increase in number of users of Social network services world-wide. Social Networking Growth by Worldwide Region June 2008 vs. June 2007 Total Worldwide Audience, Age 15+ - Home and Work Locations Source: ComScore World Metrix Unique Visitors (000) Jun-07 Jun-08 Percent Change Worldwide 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%
  • 3. 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 region the year 2007 to 2008. The overall increase was 25% Worldwide Growth among Selected Social Networking Sites June 2008 vs. June 2007 Total Worldwide Audience, Age 15+ Home and Work Locations Source: comScore World Metrix Total Unique Visitors (000) Jun-2007 Jun-2008 % Change Total 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 the year 2007-2008. During the period of 2007-2009 Facebook has the highest growth in Asian countries and Middle-East. In 2011 Facebook alone has about 600 Million users. Leading Social network service in India was Orkut till the year 2009. In June 2011 it was found that Facebook has highest number of users in India. What makes Facebook different from other leading Social network services? The answer is explained in the Danah Boyd’s research. She mentioned that Facebook is meant for kids that are a 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 of the Social network services like Myspace and Hi5 have majority (80%) of the participants that are a part of a band or they are not much educated. MySpace has most of the kids who are socially ostracized at school because they are geeks, freaks, or queers. Following Figure shows the geographic locations throughout the globe where Facebook and other Social network services have their presence.
  • 4. Figure 1: Area wise presence of Social Network services
  • 5. 2. GRAPH THEORY AND ITS APPLICATIONS IN SOCIAL NETWORK ANALYSIS Graph Theory is one of the youngest branches of Mathematics. It is used in various fields like Operations 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). V corresponds to sets of vertices and E corresponds to set of Edges. Generally the numbers of vertices 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. An edge corresponds to ties in Social networks. They depict the type of relationship between two nodes. For example: In Facebook when we add someone as a friend, we get a window stating that how you know that person (Friend, colleague, never met etc). If the person to whom I sent a request is my colleague, a relationship is formed between two nodes in the social graph as shown below figure. 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 Social network analysis, the graph will contain only those nodes that are connected to each other with some relationship. If node a had sent a request to node b to add him as a friend and node b did not accept the request, then there wont be any relationship between node a and node b. So this sub graph won’t be 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 MATRIX Vertices Vi and Vj are said to be adjacent if a link (i, j) exists between them. In the above graph 2 Node 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 this aij = aji = 1 if the vertex vi and vj are adjacent and aij = aji = 0 if vertex vi and vj are not adjacent. 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 f Table 3: Adjacency Matrix
  • 7. The adjacent matrix is used to determine relationships. A complex network graph can be broken down to a matrix for simple understanding. If every vertex is connected to every other vertex then the graph is called complete graph. This is used to find strong relationships between actors in Social network analysis. Adjacent matrix is used to find density of graph. Density can be defined as the level of completeness of graph. Density is determined by dividing number of edges or links in the graph with 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 CONNECTEDNESS Another important property of graph is Connectedness. It is defined as the ability to reach from any one of the vertex of the graph to any other vertex of the graph. Graphs with this property are called connected. The graph 2 is connected graph since we can reach from any vertex to the graph 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 person who is linked to your friend. 3. ANALYSIS OF SOCIAL NETWORK SERVICES Social Network Analysis (SNA) is basically the study of relationships between individuals or between individual and community or relationship within a group. It includes the analysis of social structures to reveal informal connections between them. The relationship between individuals is often represented in form of network. This network can be studied using Network theory. 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 is represented in form of edges or links. There can be various kinds of relationship or ties between individual actors such as friends, colleagues, neighbor, school mates etc. Social network analysis aims to explore some of the following tasks: 3.1 CENTRALITY Centrality aims to fine the most important actor in the network. In a Social network, centrality will try to find the person to which maximum of the nodes are connected in a particular network graph.
  • 8. Graph 3: Network explaining centrality The 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 in separate network. The two networks are connected by a common node that is node 3. Here we can state that the node 3 is the most important or central node. 3.2 COMMUNITIES Various actors in a Social network who shares common interests come together and form a community. A community can be of the people who support Manchester united football team or people who like to red Sidney Sheldon books. In this task we identify these communities by studying network topology. 3.3 TYPE OF RELATIONSHIP The Links between the two nodes in a Social network are of different types. Two nodes representing two persons can be linked together as Friends, colleagues, school –mates, project partners etc. In this task of SNA we identify the different types on links of an individual node to other nodes in network.
  • 9. Figure 2: Shows various types of relationships Here when a node wants to be connected to other node (Richard). We can define the type of relationship between the two nodes. Above are the types of relationships in Facebook. 3.4 NETWORK MODELING Here in this task we try to model or simulate a real world network using simple mechanisms such as graphs. We try to capture all the patterns present in the network on to the model. 3.5 ANALYZING STRONG AND WEAK TIES Every node in network graph is related or linked to some other node. The linking is call tie between 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 many common interests and spend ample amount of time with each other. In a nutshell they are close friends. For example: On Facebook, John and Rick are strongly tied if they have many common interests and friend of John is probably friend of Rick. That is they share many common friends. In the figure 4, node1, node2, node3, node4 and node5 are strongly tied to each other. Node1 is connected to node2 and node3. And also node2 and node3 are friends of each other. The nodes in a strong tie are more socially involved with each other. Ties can also lead to predict certain relationship in a network. For example: If a node A has edges to nodes B and C, then the B-C edge is especially likely to form if A’s edges to B and C are both strong ties. 3.5.2 WEAK TIES A tie between two nodes is said to be weak tie if two nodes are the given nodes are less socially involved with each other. They belong to a community that shares common interest. But they don’t have many common friends. Also they do not share many common interests.
  • 10. Graph 4: Strong and Weak Ties The type of tie between Node4 and Node6 is a weak tie. This is because they share very few common interests and friends. Let’s assume Node4 and Node6 represents two people who live in same street. They do not have any other common interests and friends. They are not very socially involved with each other. We can term the weak tie as low density network and strong tie as high density network. As stated by Mark Granovetter, weak ties are very important part of a social network. Here in the above diagram, Node4 and Node6 are weakly tied to each other. But Node4 and Node6 have their own dense networks. Thus a weak tie between Node4 and Node6 has led the two 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 never have merged. 3.5.3 BENEFITS OF WEAK TIES The research in the past 3 decades shows that the weak ties are beneficial for a number of outcomes. Weak ties also lead to knowledge development, sub-group consolidation. They also play important role in organizing larger groups that are formed by weak ties among the nodes that have their own small primary networks. Weak ties prove to be an important tool in Social Network analysis. Analyzing a large network that has millions of individuals and thousands of communities is very complex. So we can break a particular community in to sub groups on the basis of weak ties. In the figure below if we want to break up the complex network to a smaller one, we can identify the weaker ties and then separate 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 PROFILE The practical applications of the above concepts can be shown in an example, wherein a Facebook account is analyzed. While analyzing, we always consider a profile from which the analysis starts. Analyzing can be done using tools available from Internet, along with some internal 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 if both the nodes share many common interest and they frequently post on each other’s wall and most important is that they should have many friends in common. On the basis of these criteria we 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’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 24 Table 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 41 common friends, also almost all friends of Tarvinder are friend of Deepak also. Also if we observe carefully, Jaswinder Singh Randhawa has only 11 mutual friends but has rank 8. It is because the strength of a tie is not only determined by number of mutual friend but also with regards to the activity of the friend. A participant may have less mutual friend but is very active that is he continuously posts on the others wall and share comments. Such participant may get better 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 who are densely linked to each other. A social graph also helps in identifying the clusters. Clusters also help in identifying the reach ability and from one node to the other. Participants with same color 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 ANALYSIS COMMUNICATION Social network analysis of an organization helps to determine the communication flow and knowledge 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 determined that an employee ‘A’ does not have good ties with his senior ‘B’ and so he does not effectively communicate with ‘B’ instead he communicates with ‘C’ who is the head of other department. FUNCTIONING Social network analysis can determine the inter relation and functioning of various departments within an organization. TEAM BUILDING OR GROUP FORMATION SNA can help in formation of teams. SNA determines the efficiency of informal communication within a group. According the people with better bonding can be grouped together to make a strong operational team. Example of Social Network Analysis of a small organization of 5 actors: Column1 JOHN JANE AMELI ROSE DEBORAH JOHN 0 0 0 1 1 JANE 0 0 0 1 0 AMELI 0 1 0 1 0 ROSE 0 0 0 0 1 DEBORAH 0 0 1 0 0 Table 5: Communications Hierarchy of an organization revealed by SNA Here the above names are the employees of an organization. The table shows that John always goes to Rose or Deborah for any information about the sales of a product. Jane consults Rose and Ameli consults Jane and Rose. Rose consults Deborah and Deborah consults Ameli for any information. Here thus Ameli is basically the indirect or direct source of information for all the employees. After this information the organization can hire more people to assist Ameli so that her work pressure is reduced. Thus the above table also shows that the most influential person in the organization is Rose, who is consulted by three people (John, Jane and Ameli).
  • 16. 6. CONCLUSION Graphs provide visualization for almost everything. In this article we have tried to focus on the on the Social network and analysis of Social networks using Graph theory. Since 2008 the number of people on Social nets has increased considerably. The analysis of such networks gives us information about the behavior of a group and identifies informal relationships among people. Social network analysis in an organization can facilitate proper functioning of various departments, so as to minimize the friction between them. SNA can also help HR department of an organization to streamline the team formation process and optimize the operations. Applications of SNA for organizational analysis are called ONA (Organizational network analysis). ONA is upcoming field and growing very fast in the recent scenario. ACKNOWLEDGEMENT Our deepest thanks to Professor Sudipto Chakraborty for his precious guidance in writing this document. He has gone through the article and put lot of efforts to correct document when needed.
  • 17. REFERENCES 1. Vincenzo Cosenza, world map of Social Networks, December 2010. 2. Robin Wauters, It’s a Facebook World, 13 June 2011 WWW.techcrunch.com 3. Boyd danah. “Social Network Sites: Public, Private, or What?” Knowledge Tree 13 May 2007. 4. Monica Chew, Dirk Balfanz and Ben Laurie “Under mining Privacy in social Networks”. 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