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**Complex Network Theory**

Niloy Ganguly

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**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

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**Business ties in US biotech-industry**

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

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**Business ties in US biotech-industry**

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

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Internet

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Friendship Network

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**Roads and Airline Network**

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**Genetic Interaction Network**

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**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)

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**Symmetry in Complex Networks**

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**Impact of Parameters in influencing the Evolution**

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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

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**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

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**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.

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**Robustness & Stability**

Internet Robust against random failure Vulnerable against targeted attack Similar observation on Gnutella P2P network

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**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.

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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

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**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.

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**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

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**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 --

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

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