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- 1. Complex Network Analysis
- 2. What will you get to know ?

To stop the fire you have to create fire

Why do your friends seem to be more popular than you are

Are we living in a Small World

How do we detect epidemics early

Friendship network in BITS

Behavior in Online Social Networking Sites

How popular is something on DC++ - 3. Complex Networks

Non-trivial real-life networks

Observed in most Social, Biological and Computer networks. - 4. The Friendship Paradox

On an average, your friends have more friends than you do

True for all networks (or graphs).

Prominent in real life networks. - 5. The Small World Phenomenon

Any two persons in the world are connected by at most six links of acquaintances.

Among Mathematicians: Erds Number (Paul Erds)

Among Actors: Bacon Number (Kevin Bacon) - 6. http://findthebacon.com/Play.aspx
- 7. Complex Network Analysis

Diameter: Then number of links in the shortest path between furthest nodes. (Small World)

Average path-length

Degree: Number of links on a particular node(Number of neighbors) - 8. Network Density: The ratio of edges in the network to the max possible number of edges.

Density of a social network with large number of nodes is highly unlikely to exceed 0.5 - 9. Clustering Coefficient: Likelihood that two associates of a node are associates themselves

Lies between 0 and 1

Y

X

A - 10. Centrality Measures (Betweenness): The number of shortest path that passes through a node.

Synonymous with importance.

Important in study of spreading of forest fires, rumors, information, epidemics etc.

Revisit Friendship Paradox - 11. BITSian Friendship Network
- 12. BITSian Friendship Network

Network Density: 0.37

Diameter: 4

Average Path-length: 1.99

Average Clustering Coefficient: 0.51 - 13. Twitter Growth Model

With probability p, a new node(user) enters the network and links with one existing node.

With probability q = 1-p, an existing user gets linked to an existing node.

Preferential Selection:

P(deg i -> deg i+1) proportional to (i+constant) - 14. The Twitter growth model

The rate equations are: - 15. Formula vs Model Simulation
- 16. Model vs Twitter Data
- 17. Power Law!!!

Degree distribution: n(j) = c.j-

Straight line in log-log plot.

Scale free networks.

Many networks conjectured(and many found) to follow power law.

Eg.-Online Social Networks, Friendship Network, Collaboration Network (Movie-Actor, Research-Scientists), World Wide Web, Protien-Protien Interaction, Airline Networks

Pareto Principle: 80-20 rule. - 18. DC++ Search Spy

A similar approach can be applied to find out number of searches vs rank of search query.

query

keyword - 19. Power Law !!!
- 20. Rank of a keyword (node) = number of nodes with degree greater than its degree.

The inverse function gives the frequency of a keyword ranked r:

POWER LAW !!! - 21. Formula matches with the Real DC++ data