CS8803-NS
Network Science
Fall 2013
Instructor: Constantine Dovrolis
constantine@gatech.edu
http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/
Disclaimers
The following slides include only the figures
or videos that we use in class; they do not
include detailed explanations, derivations or
descriptions covered 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.
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
Reference point-1: ER random graphs
• G(n,m) and G(n,p) models (see lecture notes
for derivations)
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
Emergence of giant component
• See lecture notes for derivation of the following
Emergence of giant connected component
in G(n,p) as p increases
• https://www.youtube.com/watch?v=mpe
44sTSoF8
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
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
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
http://www.nature.com/nature/journal/v406/n6794/images/406378aa.2.jpg
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 powerlaw distribution finite?
• How to detect a power-law distribution?
• How to estimate the exponent of a
power-law distribution?
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
Bow-tie structure of directed nets
http://johncarlosbaez.wordpress.com/2011/10/03/the-network-of-global-corporate-control/
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
http://www.nature.com/nrg/journal/v5/n2/box/nrg1272_BX2.html
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?
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
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
http://en.wikipedia.org/wiki/File:EEG_mit_32_Electroden.jpg
http://en.wikipedia.org/wiki/File:Spike-waves.png
http://www.sciencedirect.com/science/article/pii/S1388245704000112
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
Course projects
plz start with the following questions
•
(and answer them in your project proposal)
Do you want to do a research-oriented project?
•
What is the nature of the involved work?
•
Do you want to do something domain-specific or general?
•
Which topic of the course syllabus is your project most relevant to?
•
Solo or group project?
•
Some possible project types:
– 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)
– Data collection, data analysis, simulation, math analysis, a combination of these?
– E.g., related only to computer networks? Social nets? Brain nets?
– Or something general (e.g., an algorithm for community detection in general nets)
– Have you read 1-2 papers about that topic?
– Which are the strengths or complementary backgrounds in your group?
– 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
Duncan Watts (from the small
world ‘98 paper) will talk to us
about computational social
science
http://www.youtube.com/watch?v=D9XF0QO
zWM0