Here is the slides on redistribution models that we have covered in the class.

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Here is the slides on redistribution models that we have covered in the class.
In the following weeks, we will cover several papers related to robustness and cascading failures in complex networks. This week (Oct 18 – 22), Sindhura will cover the following three papers:
1. Error and Attack Tolerance of Complex Networks
2. Optimization of Robustness of Complex Networks.
3. A simple model of global cascades on random networks
More papers on cascading failures that we plan to cover are as follows:
1. A. E. Motter and Y. Lai “Cascadebased Attacks on Complex Networks” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 66, 2002
2. R. Albert, I. Albert and G. L. Nakarado “Structural Vulnerability of the North American Power Grid” Rev. Mod. Phys., 69, 2004
3. Cascadebased attack vulnerability on the US power grid
4. Optimizing complex networks for resilience against cascading failure
5. Ali Pinar, Juan Meza, Vaibhav Donde, and Bernard Lesieutre. Optimization strategies for the vulnerability analysis of the electric power grid. SIAM Journal on Optimization, 20(4):1786–1810, 2010.
6. Cascading failure spreading on weighted heterogeneous networks
7. K. Peters, L. Buzna and D. Helbing “Modelling of Cascading Effects and Efficient Response to Disaster Spreading in Complex Networks” International Journal of Critical Infrastructures 2008, 4(1/2):46–62,
2008
8. D. E. Newman, B. Nkei, B. A. Carreras, I. Dobson, V. E. Lynch and P. Gradney “Risk Assessment in Complex Interacting Infrastructure Systems” 38th Annual Hawaii International Conference on System
Sciences, 2005
9. B. A. Carreras, D. E. Newman, P. Gradney, V. E. Lynch, and I. Donson, “Interdependent Risk in Interacting Infrastructure Systems,” Proc. of the 40th Hawaii International Conference on System Sciences, 2007.
10. L. Buzna, K. Peters and D. Helbing “Modelling the Dynamics of Disaster Spreading in Networks” Physical A., 328:132–140, 2006
11. Z. Dezso and A. L. Barabasi “Halting Viruses in ScaleFree Networks” Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 65, 2002
The project must be done by following this procedure.
This paper provides a nice view on complex networks. Please read it.
SIAM REVIEW Vol. 45,No . 2,pp . 167–256
The Structure and Function of Complex Networks
Team 1. Thang Dinh and Yilin Shen
Team 2. Nam Nguyen and Dzung Nguyen
Team 3. Ying Xuan and Sindhura
In this sequence of lectures, we are going to cover several models as follows:
1. Random graph model. (Presented by Yilin Shen). Lecture notes can be found here
2. The BarabasiAlbert Model
3. Modifications to the BarabasiAlbert Model
4. Fitness based Model
5. Online and Offline Models (presented by Nam Nguyen)
6. SmallWorld Model
(Some other models that we are not going to cover in this class, including Copying models and graph from optimization principles)
Continue reading
I will cover a little bit of history in this entry. Yilin Shen will present the random model in the class. Please read the first two papers in the reading list. In addition, you are required to understand the binomial distribution and its asymptotic behavior, Chernoff inequalities, a concentration inequality. Please read paper 11 for this (Concentration Inequalities and Martingale Inequalities). This is a fundamental knowledge for you to understand the course! So please do read and study paper 11!
In 1999, at the dawn of the new Millennium, a most surprising type of graph was uncovered, thus brought graph theory to the heart of a new paradigm of science. This family of graphs consists a wide range of applications, from WWW, biological networks, phone call networks, collaboration networks, to social networks… These graphs have the following main characteristics:
As you can see, the first two characteristics come naturally and the third one has long been within the mindset. The most remarkable fact is the last one, the power law, which allows us to use one single parameter, , to describe the degree distribution of billions of nodes. This discovery leads to two things: (1) Reinvestigate many existing tools such as combinatorial, probabilistic and spectral, to deal with problems on power law graphs; and (2) these graphs provide insight and suggest many new research direction in the field of graph theory.
Indeed, even at the end of the 19th century, the power law had been noted in various scenarios. However, only in 1999 were the dots connected and a more complete picture emerged. Since then, a new area of network complexity has been rapidly developing, spanning several disciplines such as mathematics, physics, computer science, social science, biology, and telecommunication.
Here is a brief history on what happen before 1999 on the power law:
Here is the tentative list of papers which we will partially cover in the class. It will be updated regularly.
Influence in Social Networks
Network Vulnerability and Robustness
Dynamic Communities
Welcome to the class! Here is a short description of the syllabus.
General Information:
Course Description and Objectives
The scope of this class is to offer the basic theory of complex networks with a focus on optimization techniques, in the design and analysis of these networks. In addition, it also covers a wide range of applications and optimization problems arising in online social networks and complex communication networks.
I plan to cover the following:
Prerequisites
There is no formal prerequisite for this course. However, this course is designed mainly for graduate students whose research interests lie in complex networks. Students are expected to be very selfmotivated and able to keep up with the reading and presentations.
Textbooks
No textbook is used in this course. We will read a list of related papers along with my notes. For references, please read the following:
Grading Policies
There will be one project and some presentations. There is no homework assignment in this class. For cutoff points: A >= 85%, 85% > B >= 75%, 75% > C >= 65%