NETWORK THEORYBy:

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

Networks don’t grow accidently ..they evolve according to some pattern

The Secret of Networks

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 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).

Degree Centrality

• 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.

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

Betweenness

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.

Closeness

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.

Eigenvector Centrality

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.

Social Network Analysis

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

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.

Degree Distribution

• 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.

Network Resilience

• 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.