2 Complex Networks ? Real-World Networks (as Complex Networks) Large network sizeHeterogeneous network elementsDiverse interconnection patternHighly DynamicDifficult to AnalyzeComplex Network TheoryAn active area of scientific research inspired largely by the empirical study of real-world networksProvides tools to understand and analyze complex networks through simple equations
3 Business ties in US biotech-industry Nodes: investment, pharma, research labs, public, biotechnologyLinks: financial, R&D collaborations
4 Business ties in US biotech-industry Nodes: investment, pharma, research labs, public, biotechnologyLinks: financial, R&D collaborations
9 Questions to ponder upon.. Is there any symmetry displayed by these networksHow 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)
11 Impact of Parameters in influencing the Evolution
12 Small World EffectA 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 pointInitial senders in Omaha, NebraskaEach sender was asked to forward a packet to a friend who was closer to the targetFriends asked to do the sameResult: Average of ‘six degrees’ of separationS. 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 InternetRobust against random failureVulnerable against targeted attackSimilar 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 Twitter6 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 efficientUnderstanding the evolution of Online Social NetworksUnderstanding the community structure of OSNs and adding features like Recommendation systemAnalyzing 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 ModelsRandom networks, power-law networks, small world networksVarious Processes taking place on these networksEvolution, Search, Attacks, Epidemics etc.Case study on OSNs and P2P networks
20 Course Details Teaching Assistant Books Animesh Srivastava Sourav DandapatJoydeep ChandraBooksComplex Networks – Structure, Robustness and FunctionsReuven Cohen and Shlomo HavlinStructure and Functions of NetworksNewman, Stogatz and BarabasiOnline Video --
21 Course StructureMid-sem : 20 Term Project/ (Scribes, Assignment) : 35 Class Performance (Attendance etc): 5 End-sem : 40