What is Social Network?
• Social Network is defined as a network of relationships
or interactions, where the nodes consist of people or
actor, and the edges or archs consist of the
relationships or interactions between these actors.
• In fact, social network offers a platform to people for
sharing knowledge, thought or opinions and more often
to maintain societal relationship.
• There can be several types of social networks like email
network, telephone network but recently online social
network like Facebook, Twitter, LinkedIn, Instagram etc.
have gained much popularity.

Social Network
Actors/
Users
Actors/Users
Adil Arsalan Hasan Shahid Nafees Abdur
Rahman
Sajid
Adil -- 1 0 0 1 1 0
Arsalan 1 -- 0 0 1 0 0
Hasan 0 0 -- 0 0 1 1
Shahid 0 0 0 -- 1 0 0
Nafees 1 1 0 1 -- 0 0
Abdur
Rahman
1 0 1 0 0 -- 1
Sajid 0 0 1 0 0 1 --
As an alternative representation, adjacency matrix delineated
in above table
A real social network can be combination of four
variants i.e,
a) A social network with homogenous nodes and
undirected associations
b) A social network with homogenous nodes
connected through directed and undirected
associations
c) A social network with heterogenous types and
weights of associations
d) A social network with heterogenous nodes in
terms of types and weights

What is Social Network Analysis?
Social Network Analysis is the methodical analysis of social networks.
It views social relationships in terms of network theory, consisting of
nodes(representing individual actors within network) and ties (which
represent relationships between the individuals, such as friendship,
organisational position ).
Social Network Analysis analyses the structural properties of
individual or groups of individuals in a network.
These measurements not only depict perspectives of the
interconnections and relationships amongst various individuals but
also consider the effect of these interconnections on each other as
well as on the group of interconnected individuals.
Analysis tasks of social networks includes following:
• Discovering the structure of social network
• Finding various attribute values for the network- Ex. radius,
diameter, centrality, betweenness, shortest paths, density etc
• Finding communities in the social network
• Visualizing the whole or part of the social network

There are two basic kinds of social network analysis
• Ego network analysis is concerned with analysis of individual
nodes. A network can have as many egos as nodes in the graph.
Egos can be persons, organizations or whole society. In ego
network analysis, individual behaviour and its variation is
mined and described.
• Complete network analysis is concerned with the analysis of
all the relationships among a set of nodes. Techniques such as
subgroup analysis, equivalence analysis and measures like
centrality (closeness, degree, and betweenness) all require
complete networks.
Kinds of Network Analysis

 The field of social networks and their analysis has evolved
from graph theory, statistics and sociology and it is used in
several other fields like information science, business
application, communication, economy etc.
 Analysing a social network is similar to the analysis of a graph
because social networks form the topology of a graph. Graph
analysis tools have been there for decades. But they are not
designed for analysing a social network graph which has
complex properties.
 Social networks are dynamic i.e. there is continuous evolution
and expansion.
 A node in social network usually has several attributes.

 Online Social Network have been emerging, developing
and changing exponentially.
 Huge development in social networks leads to the
growing need for social network mining.
Why we chose this project?

Why we chose this project?
• Research is being done on impact of OSN on
future internet.
• Combating terrorism is one of the fields
where SNA techniques are used.
• SNA can be integrated to other popular
fields such as WWW, blogosphere, semantic
web.
• SNA techniques are being successfully
applied to disaster management.

Social Network Analysis Tools
Social Network analysis tools are used to identify, analyze,
visualize or simulate nodes (organizations, or knowledge) and
edges (relationship or interaction) from various types of input
data including mathematical models of social networks.
Four major analysis tools
1.Gephi
2.Networkx
3.IGraph
4.Pajek

:
1. Gephi
It is an interactive visualization and exploration platform for
all kinds of networks, dynamic and hierarchical graphs.
It runs on Windows, Linux and Mac OS X.
2. Networkx
It is a Python language software package for the creation,
manipulation and the study of structure and functions of
the complex networks.
It can be used to
• generate many types of random and classic networks,
• Analyze network structure,
• Build network models
• Draw networks etc.

3. IGraph
It is a free software package for creating and manipulating
graphs.
It includes implementations for classic graph theory problems
like minimum spanning trees and network flow. It’s efficient
implementation allows it to handle graphs with millions of nodes.
4. Pajek
It is a widely used Software for drawing networks.
It also has analytical capabilities, can be used to compute most
centrality measures, identify structural holes, block-model etc.

Tools Comparison
:
The four tools are compared on the following six criterion –
platform, Graph types, algorithm time complexity, graph
layout, graph input file format, graph features

ATTRIBUTES OF SOCIAL NETWORKS FOR SNA
SNA is primariIy based on several attributes, some of which are defined
as characteristics of graphs and some as distribution of information and
behavior of actors.
 Degree
Degree of a node is the number of edges connecting this node with
other nodes if graph is undirected. Whereas if graph is directed then a
node has in-degree defined as number of incoming edges and out
degree defined as number of outgoing edges. Social network
researchers have always been concerned with the degree of node.
The distribution of node degree in a network follows the power law.
More precisely,
Pk α k-α
Pk is the probability that a node has a degree k, and a is a constant and
usually a is a value between 1.6 and3.0

 Geodesic Distance and Diameter
For both directed and undirected graph, the geodesic distance is
the number of edges in the shortest possible walk from one actor
to another. The diameter of a network on the other hand is the
largest geodesic distance in the (connected) network.
 Cliques and Subgroups
To understand that how the network is likely to behave, it is
necessary to partition the actors into cliques or "sub-groups".
• clique is simply a sub-graph in which all nodes are more closely
tied to each other than they are to actors who are not part of
the sub-graph. If the sub-graph is complete-graph (there exists
every possible tie among nodes) then it is called maximal
clique
 Maximum Flow
This flow shows that the strength of a tie between two actors
depends on the weakest link in the chain of connections.
 Centrality
Centrality is a measure that quantifies the influence of an actor in
the network.
 Many approaches have been identified to define centrality.
Three of which are most relevant - degree, closeness and
betweenness centrality

 Degree Centrality
It is most common centrality measure in which centrality of a node depends on the
number of nodes attached to it directly.
For a network with g nodes, the degree centrality of node attached to it directly. For a
network with g nodes, the degree centrality of node
The degree of a node, denoted by d(n) is the number of nodes adjacent to it. Apparently,
a node's degree centrality is a count ranging from 0 to g-l.
The degree centrality of node ni after normalization is:
cd(n)= d(n)/(g-l)
 Closeness Centrality:
Closeness centrality overcomes this shortcoming by considering the sum of the geodesic
distances between a given node and the rest. For the network with g nodes, the closeness
centrality of node ni is defined as following
where, d(ni-nj) is the number of edges in the geodesic linking ni and nj Closeness
centrality is normalized

 Betweenness Centrality:
Betweenness centrality measure highlights those nodes who fall
in the connecting path of many nodes. For a network with g
nodes, the betweenness centrality for node
Here,gjk is the number of the shortest paths linking two nodes in the
network gjk(n i) is the number of shortest path linking two nodes that
go through the node n i. Clearly, maximum number of such paths is
(g-l )(g-2)/2. Therefore betweenness centrality is normalized as

 Small World Effect
Small World Effect describes the distance between any pair of nodes is much
smaller than the size of the network.
 Clustering Coefficient
A triplet is an ordered set of three vertices, (i, v, j), where v is considered the focal
point and there are undirected edges <i, v> and <v, j>. An open triplet is defined as
three vertices in which only the required two are connected. A closed triplet is
defined as three vertices in which there are three edges.
Where, Tv the close triplet count around v. and Dv the degree of v (number of
adjacent vertices).

Analysis of Facebook Social Network
Facebook use basic elements of SNA to identify and
recommend potential friends based on friends of
friends.
This study aims to explore the following concepts:
 Representation of the facebook network
 Identify the high degree nodes in the network
 Behaviour of high degree nodes in the facebook
network.
This work consists of two phases. First, a subgraph
consisting of high-degree nodes (i.e. users having large
number of friends) was obtained from a facebook
social graph. Secondly, the attributes of these high
degree nodes were analyzed using the Social Network
Analysis tool called GEPHI.

Visualization
 Gephi is an open source software for graph and network analysis. The
visualization module uses a special 3D render engine to render graphs in real-
time. This technique uses the computer graphic card, as video games do, and
leaves the CPU free for other computing.
 It supports highly configurable layout algorithms like Force Atlas algorithm.
 Force Atlas makes the connected nodes attracted to each other and pushes
unconnected nodes apart to create clusters of connections. This SNA tool
provides Ranking and partition data that makes the network meaningful.
 In our study the final subgraph file was converted to CSV format and imported
to GEPHI tool for obtaining various patterns and parameters related to the high
degree nodes.

Results
Average Degree
The degree distribution of the nodes of the sub-graph
is shown in figure. Average degree of the sub-graph is
1.778.

Connected Components
The number of connected components obtained is equal to 2348. 1872 nodes are not
connected to any nodes. The largest component contains 2940 (46.96 %) nodes and
4485 (80.56%) edges
Network Diameter
The diameter of the largest component is 34 nodes. total number of shortest paths is
8645958 and average path length is 14.177

Modularity
Figure 5 shows the size distribution of modularity classes of the sub-graph
leaving all the unconnected nodes. There are total 511 communities and
modularity is 0.933.

Average Clustering Coefficient
Average clustering coefficient of the sub-graph is 0.132, which is shown in Figure 6.

CONCLUSION
 In this preliminary work, we focused on the study of a
subgraph of Facebook social network that contains
the high-degree nodes i.e. for which the number of
friends is higher.
 We found that there are little direct friendship
relations among these high degree nodes.
 Though their friendship relations are very high in the
Facebook graph, but relationship among them is less.
 Owing to the memory limitations in GEPHI tool, we
have analyzed a subgraph of facebook social graph.
 Gephi has memory limitations and it is less efficient
in the matter of allowed vertices.
 A future analysis can be done in an incremental way
i.e. the facebook social graph can be subdivided into
different parts and results can be obtained by
combining the analysis done on separate parts.

Future Work
It is a well-known fact that the web pages are hyper linked to other
web pages and further to leverage the existence of hyperlinks, web
is modeled as graph where web pages represent the vertices and
subsequent hyperlinks form the edges. Therefore, web can be
treated as a perfect example of social network and to add to this
analysis, PageRank algorithms used by Google search engine and
HITS can be seen as applications of SNA.

Social Network Analysis (SNA) 2018

Social Network Analysis (SNA) 2018

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Social Network Analysis (SNA) 2018