1. By: Roma Mohibullah Shahrukh Qureshi
Network Theory
By:
Roma Mohibullah
Shahrukh Qureshi

2. 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.

3. Examples of networks Internet Neural networks Supply chain network
The solar system
Colleagues

4. 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

6. 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.

9. 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

11. 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

12. what happens when we bring the world wide web into the picture?

14. 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

16. The Secret of Networks
Networks don’t grow accidently ..they evolve according to some pattern

18. Centrality

19. 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.

20. There are four measures of centrality that are widely used in network analysis:
Degree centrality
Betweenness
Closeness
Eigenvector centrality.

21. 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).

22. 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.

23. Betweenness
A node which connects two sub networks or isolated nodes to the rest of the network.

24. 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.

25. 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.

26. 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.

27. 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

29. 2 other properties:
Degree Distribution
Network Resilience

30. 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.

31. 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.

32. One way to remove the nodes in a network is to random removal
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.