NETWORK THEORY
By:
Roma Mohibullah
Shahrukh Qureshi
WHAT IS NETWORK THEORY?

Network theory is an area of applied mathematics and
network science.

Study of graphs as a representation of relations between
objects

Applications in physics, computer
science, biology, economics, operations research,
and sociology.
EXAMPLES OF NETWORKS

Internet

Neural networks

Supply chain network

The solar system

Colleagues
SOCIAL NETWORK THEORY

Study of how the social structure of relationships around a
person, group, or organization affects beliefs or behaviors

traditional sociological studies  it is the attributes of
individual actors -- whether they are friendly or unfriendly,
smart or dumb, etc. -- that matter.

Social network theory  the attributes of individuals are less
important than their relationships and ties with other actors
within the network

Focus on properties of relations of a unit, instead of the
properties of the unit itself
SOCIAL NETWORK THEORY (CONT.)

Social network theory views social relationships in terms
of nodes (actors) and ties (relations)

a social network is a map of all of the relevant ties
between the nodes being studied.

Relationships can comprise of feelings, the exchange of
information, or more tangible exchanges such as goods
and money

The network can also be used to determine the social
capital of individual actors.
SOCIAL CAPITAL
social networks have value (financial, educational etc.)
 social contacts affect the productivity of individuals and
groups

Credit Ratings
 Advertising – based on social circle
 Business growth opportunities

COMMUNICATION NETWORK THEORY

Networks depicting the flow of communication

Example of organizational communication network

Identify Place employees have in the communication network

Identify exposure to and control over information

Identify bottlenecks

these relationships may also help to explain why employees develop
certain attitudes toward organizational events or job-related matters
WHAT HAPPENS WHEN WE BRING THE WORLD WIDE
WEB INTO THE PICTURE?
SOCIAL NETWORKING THROUGH INTERNET

Orkut, facebook, twitter, linkedin, myspace, youtube..

Our social networks are bigger than we could have ever
imagined

Provides greater opportunities for people and
businesses
Finding love
 Finding job
 Finding friends
 Exploring business opportunities

The Secret of Networks
Networks don’t grow accidently ..they evolve according to some pattern
Centrality
Centrality determines the relative importance of a node
within the network
For example, how important a person is within a social
network, or, in the theory of space syntax, how important
a room is within a building or how well-used a road is
within an urban network.
There are four measures of centrality that are widely used in
network analysis:
•
Degree centrality
•
Betweenness
•
Closeness
•
Eigenvector centrality.
Degree Centrality
• Degree centrality is defined as the number of links incident upon a node
(i.e., the number of ties that a node has).
• Degree is often interpreted in terms of the immediate risk of node for
catching whatever is flowing through the network (such as a virus, or some
information).
• A high centrality degree is called a hub.
• If the network is directed (meaning that ties have direction), then we usually
define two separate measures of degree centrality, namely indegree and
outdegree.
• Indegree is a count of the number of ties directed to the node, and
outdegree is the number of ties that the node directs to others.
• For positive relations such as friendship or advice, we normally interpret
indegree as a form of popularity, and outdegree as gregariousness.
Betweenness
A node which connects two sub networks or isolated nodes to the rest of the
network.
Closeness
In the network theory, closeness is a sophisticated measure of
centrality. It is defined as the mean geodesic distance (i.e., the shortest
path) between a node v and all other nodes reachable from it.
Eigenvector Centrality
Eigenvector centrality is a measure of the importance of a node in a network.
It assigns relative scores to all nodes in the network based on
the principle that connections to high-scoring nodes contribute more to the score of
the node in question than equal connections to low-scoring nodes.
Social Network Analysis
Granovetters Theory of Strength of Weak Ties states that an
individual's social network, specifically those who are only
acquaintances are better at helping the individual obtain
employment than are close personal friends or family.
6 Degrees Of Separation
• “Each node in a network is six or less nodes away from the other
nodes”
• This implies the speed with which information travels in a
network
2 other properties:
• Degree Distribution
• Network Resilience
Degree Distribution
The degree of a node in a network is the number of connections it has
to other nodes and the degree distribution is the probability
distribution of these degrees over the whole network.
Network Resilience
• The resilience of network means the removal of its nodes, which is related to
the concept of degree distributions.
• The function and structure of a network usually rely on its connectivity. Once
some nodes are removed, the length of paths could be increased, even the
network becomes disconnected. However, there are a different ways to remove
the nodes.
• One way to remove the nodes in a network is to random removal. This
approach wouldn't affect the distances between nodes almost since most nodes
in a network have low degree and therefore lie on few paths between others.
• The other way to remove nodes from networks is targeted at high-degree
nodes. Needless to say, it will have tremendous effects on the structure of a
network. And the distance would increase acutely with the fraction of nodes
removed.