Lecture 8

Social Data Modeling

Lecture 1

Textbooks

Lecture 2

Assignments & Project

	Assignment 1
	Assignment 2
	Assignment 3
	Project Assignment A
	Project Assignment B
	About Evaluations

Lecture 3

Course Overview

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Page last edited by Sune Lehmann Jørgensen (sljo) 02/04-2013

Program

Today's lecture is about network analysis. More specifically, we'll focus on simple models for network structure. And because I love networks, we'll also spend a bit of time covering networks more generally.

Reading

Today's reading.

For the lecture you'll need to know about preferential attachment, scale free networks and the Barabasi-Albert model.
To work with the models, we'll use networkx. This page will take you to installation instructions: http://networkx.github.com and this page is where the tutorial can be found: http://networkx.github.com/documentation/latest/tutorial/
An overview corresponding to today's topics can be found in the first three chapters of Network Science by Laszlo Barabasi. We'll put a special empahsis on chapter 3 (everything except advanced topics). The book can be downloaded here in various forms: http://barabasilab.neu.edu/networksciencebook/index.html

Exercise 1. Reading and NetworkX

If you don't already know the module, work through the NetworkX tutorial - trying out the various commands on your own.
Answer the following questions in your own words (look the answers up online - e.g. using the wikipedia links above): What does clustering mean to a network scientist? What does it mean that a network is a "small-world"? (hint: remember to include clustering in your answer). What is the network degree distribution? What is a power-law? Name a few examples of networks with power-law degree distributions.

Exercise 2. The Barabasi-Albert (BA) model in NetworkX.

Use NetworkX to code up the BA model. Start with 5 nodes connected at random. Add one node at a time and have each new node connect to 3 existing nodes. Keep track of the age of each node (e.g. by naming the nodes by the time-step they've been introduced). Hint: The trickiest thing about coding up this model is choosing a node with probability proportional to its degree. First, you will need to to be able to choose stuff at random: use this module. Now, the easiest way that I can think of to do this is to create a list with each node occurring with its degree and simply picking a random node from this list (but maybe you can find a better way). [It's possible to create BA networks with a builtin NetworkX function - that's not ok - you must write the code on your own].
Once you've generated a network of 300 nodes, use NetworkX and matplotlib to plot the network.
Now, create a new network of 5000 nodes and plot the degree distribution (use both loglog and linear scales). Hint: To see an example of plotting a network degree distribution, check out pp 26-28 here: http://www.stanford.edu/class/cs224w/nx_tutorial.pdf .
Fit the data in the 5000 node network to find the slope of the straight line in the log-log plot. [Hint: linear regression in python]. Generate 200 networks and fit each one - what's the average value and variance across for all slopes? Does that answer correspond to what you expected to find, according to the theory?
Age. Calculate the average degree as a function of node-age for your 200 networks. (What is the average degree of all of the oldest nodes, what's the average degree of all the second-oldest nodes, what's the average degree of all the the third oldest nodes, etc). Create a plot of average degree on the y-axis and node-age on the x-axis. Is this the picture you expect to see in real-world networks? Justify your answer.
Do you think the BA model is a good model for real-world networks? Explain the reasons for your anwer.

Advanced reading (will help you answer some of the questions above)

Adamic and Huberman (2000). Power law distribution of the World Wide Web. Science, 287:2115. Download here, helps with the age-question.
Goldstein, Morris, Yen (2004). Problems with fitting to the power-law distribution. Eur. Phys. J. B 41, 255–258 (2004). Download here. Helps with problems with fitting power-laws question.

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