NILOY GANGULY Complex Network Theory
Mar 31, 2015
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