1. Complex Network Theory
Niloy Ganguly

2. Complex Networks ? Real-World Networks (as Complex Networks)
Large network size
Heterogeneous network elements
Diverse interconnection pattern
Highly Dynamic
Difficult to Analyze
Complex Network Theory
An active area of scientific research inspired largely by the empirical study of real-world networks
Provides tools to understand and analyze complex networks through simple equations

3. Business ties in US biotech-industry
Nodes: investment, pharma, research labs, public, biotechnology
Links: financial, R&D collaborations

4. Business ties in US biotech-industry
Nodes: investment, pharma, research labs, public, biotechnology
Links: financial, R&D collaborations

5. Internet

6. Friendship Network

7. Roads and Airline Network

8. Genetic Interaction Network

9. Questions to ponder upon..
Is there any symmetry displayed by these networks
How have these networks emerged
Are there any properties based on which one network can be differentiated from the other
Are these networks robust against failure
Are these networks helpful in information flow
How can we engineer (build) such network (engineering complex systems)

10. Symmetry in Complex Networks

11. Impact of Parameters in influencing the Evolution

12. Small World Effect
A Facebook-platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between different people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees.
Social Web App from Facebook

13. Small World Effect Milgram’s small world experiment:
Even in very large social networks, the average distance between nodes is usually quite short.
Milgram’s small world experiment:
Chose individuals in the U.S. cities of Omaha, Nebraska and Wichita, Kansas to be the starting points and Boston, Massachusetts to be the end point
Initial senders in Omaha, Nebraska
Each sender was asked to forward a packet to a friend who was closer to the target
Friends asked to do the same
Result: Average of ‘six degrees’ of separation
S. Milgram, The small world problem, Psych. Today, 2 (1967), pp

14. Watts-Strogatz ‘Small World’ Model (Simple Rules)
Watts and Strogatz introduced this simple model to show how networks can have both short path lengths and high clustering.
D. J. Watts and S. H. Strogatz, Collective dynamics of “small-world” networks, Nature, 393 (1998), pp. 440–442.

15. Robustness & Stability
Internet
Robust against random failure
Vulnerable against targeted attack
Similar observation on Gnutella P2P network

16. Investigating 9-11 Terrorist Attack
Social Network Analysis is a mathematical methodology for connecting the dots - using science to fight terrorism. Connecting multiple pairs of dots soon reveals an emergent network of organization.

17. DDoS Attack on Twitter
6 Aug 2009: BesidesTwitter, Facebook, Youtube and Live Journal were also attacked on the same day. Complex network analysis showed one common target in all these attacks whose online name is cyxymu.
Details can be found at

18. Some Interesting Problems
Building networks which are robust as well as efficient
Understanding the evolution of Online Social Networks
Understanding the community structure of OSNs and adding features like Recommendation system
Analyzing the growth of Movie-Actor networks, Collaboration networks, Transportation networks etc.

19. Course Outline Network Measurements Network Models
Clustering coefficient, assortativity coefficient, node centrality measures, betweenness measures, community identification, graph spectra etc.
Network Models
Random networks, power-law networks, small world networks
Various Processes taking place on these networks
Evolution, Search, Attacks, Epidemics etc.
Case study on OSNs and P2P networks

20. Course Details Teaching Assistant Books Animesh Srivastava
Sourav Dandapat
Joydeep Chandra
Books
Complex Networks – Structure, Robustness and Functions
Reuven Cohen and Shlomo Havlin
Structure and Functions of Networks
Newman, Stogatz and Barabasi
Online Video --

21. Course Structure
Mid-sem : 20 Term Project/ (Scribes, Assignment) : 35 Class Performance (Attendance etc): 5  End-sem : 40