Presentation Transcript

1. CS8803-NSNetwork ScienceFall 2013

   Instructor: Constantine Dovrolis constantine@gatech.edu http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/
2. Disclaimers The following slides include only the figures or videos that we use in class; they do not include detailed explanations, derivations or descriptionscovered in class. Many of the following figures are copied from open sources at the Web. I do not claim any intellectual property for the following material.
3. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
4. Reference point-1: ER random graphs G(n,m) and G(n,p) models (see lecture notes for derivations)
5. Emergence of giant connected component in G(n,p) as p increases http://networkx.lanl.gov/archive/networkx-1.1/examples/drawing/giant_component.html
6. Emergence of giant component See lecture notes for derivation of the following
7. Emergence of giant connected component in G(n,p) as p increases https://www.youtube.com/watch?v=mpe44sTSoF8
8. Reference point-2: Regular graphs Ring lattice with k connections to nearest neighbors (see lecture notes) http://www.learner.org/courses/mathilluminated/units/11/textbook/04.php
9. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
10. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
11. http://www.nature.com/nature/journal/v406/n6794/images/406378aa.2.jpg http://www.nature.com/nature/journal/v406/n6794/images/406378aa.2.jpg
12. More about power-laws(see derivations in class notes) Power-laws are everywhere (“more normal than the Normal distribution”) When is the m’th moment of a power-law distribution finite? How to detect a power-law distribution? How to estimate the exponent of a power-law distribution?
13. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
14. Bow-tie structure of directed nets http://johncarlosbaez.wordpress.com/2011/10/03/the-network-of-global-corporate-control/
15. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
16. http://www.nature.com/nrg/journal/v5/n2/box/nrg1272_BX2.html
17. How to control β and γ? The paper presents a stochastic model to do so But there are many other models that can do the same What is the main “ingredient” to get a power-law degree distribution? What is the main “ingredient” to get a hierarchical structure?
18. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
19. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
20. http://en.wikipedia.org/wiki/File:EEG_mit_32_Electroden.jpg
21. http://en.wikipedia.org/wiki/File:Spike-waves.png
22. http://www.sciencedirect.com/science/article/pii/S1388245704000112 http://www.sciencedirect.com/science/article/pii/S1388245704000112
23. Outline As a reference point: Poisson random graphs Regular graphs Common properties of real-world networks Size of largest connected component Small-world property Heavy-tailed degree distribution Hierarchical organization Network motifs Application paper: Small-world networks and functional connectivity in Azheimer’s disease Discuss course projects – project proposals due in a week Collect email addresses Surprise “visitor” will talk about Sociology and NetSci
24. Course projectsplzstart with the following questions (and answer them in your project proposal) Do you want to do a research-oriented project? Ok to work on something that relates to your research area Not ok to submit something you have already done Ok to do something that has no clear research potential (e.g., to reproduce the results of a published paper or to develop a tool that can be used in netsci research) What is the nature of the involved work? Data collection, data analysis, simulation, math analysis, a combination of these? Do you want to do something domain-specific or general? E.g., related only to computer networks? Social nets? Brain nets? Or something general (e.g., an algorithm for community detection in general nets) Which topic of the course syllabus is your project most relevant to? Have you read 1-2 papers about that topic? Solo or group project? Which are the strengths or complementary backgrounds in your group? Some possible project types: Reproduce the main results of a research paper with a different dataset(s) Model a system that you understand well as a network and formulate some key questions about that system as network-related questions Develop a simulator for a network model (ideally involving some sort of dynamics on the network) and investigate some concrete questions computationally Develop an actual system (e.g., Web application) that will allow us to collect data about a network process in the background (e.g., a social game of some sort) Prove analytically a property of a network model that has been shown only numerically in the published literature
25. Duncan Watts (from the small world ‘98 paper) will talk to us about computational social science http://www.youtube.com/watch?v=D9XF0QOzWM0