NILOY GANGULY

Complex Network Theory

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

Business ties in US biotech-industry

Nodes: investment, pharma, research labs, public, biotechnologyLinks: financial, R&D collaborations

http://eclectic.ss.uci.edu/~drwhite/Movie/

Business ties in US biotech-industry

http://eclectic.ss.uci.edu/~drwhite/Movie/

Nodes: investment, pharma, research labs, public, biotechnologyLinks: financial, R&D collaborations

Internet

Friendship Network

Roads and Airline Network

Genetic Interaction Network

Questions to ponder upon..

Is there any symmetry displayed by these networks

How have these networks emergedAre there any properties based on which one

network can be differentiated from the otherAre these networks robust against failureAre these networks helpful in information

flowHow can we engineer (build) such network

(engineering complex systems)

Symmetry in Complex Networks

Impact of Parameters in influencing the Evolution

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

Small World Effect

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. 60-67

Watts-Strogatz ‘Small World’ Model (Simple Rules)

D. J. Watts and S. H. Strogatz, Collective dynamics of “small-world” networks, Nature, 393 (1998), pp. 440–442.

Watts and Strogatz introduced this simple model to show how networks can have both short path lengths and high clustering.

Robustness & Stability

Internet Robust against random

failure Vulnerable against

targeted attack

Similar observation on Gnutella P2P network

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.

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 http://blogs.mcafee.com/mcafee-labs/collateral-damage

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.

Course Outline

Network Measurements 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

Course Details

Teaching Assistant 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 -- http://www.facweb.iitkgp.ernet.in/~niloy/

Course Structure

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