CS 765 Complex Networks
Network Lab 4
Due on Thursday Oct 27, 2016 at 2:30 pm
Random graphs and giant components (2 points)
Growing networks: preferential and random growth (3 points)
- Go to http://ccl.northwestern.edu/netlogo/models/GiantComponent
and launch the applet. Click 'setup' and then 'go'.
- Try it with 80 nodes and then 400 (if your computer can not compute, use smaller node sizes).
Observe what happens right around the point where the average degree is 1 (the vertical line in the plot).
Comment about the variation in the size of the largest component as you increase the number of edges/nodes.
Open the NetLogo applet:
Click on 'setup' to start out with a cycle of 5 vertices.
Click on 'go-once' to add vertices one by one, each with m edges. Play with the m and gamma parameters.
The Watts Strogatz small world model (2 points)
- Select m=1 and gamma=0. Add 300 vertices. Click on the 'resize nodes' button to size the vertices by their degree.
Repeat the same, but with m = 1 and gamma = 1. What differences do you observe between the two networks,
e.g. in terms of appearance, the number of vertices with degree 1, and the maximum degree of any vertex?
- Generate two networks with 1000 vertices and m = 4. (You can run this faster by adjusting the speed slider at the top.)
For one network select gamma = 0, and for the other gamma = 1. Which degree distribution looks more like a power law?
Go to http://ccl.northwestern.edu/netlogo/models/SmallWorlds.
This is a NetLogo model that will allow you to vary the rewiring probability.
LexRank (3 points)
- Adjust this probability from 0 to 1, each time hitting "rewire" and allowing it to calculate the clustering coefficient and average path length.
Does your plot agree with what you saw in lecture?
Try using a spring layout. In what ways do the random links make the world smaller?
Select a piece of text (10-20 sentences) that you would like to summarize and paste it in the appropriate box of the
If you are unable to paste text into the text box, try a different browser.
Submitting your files
- There are two parameters you can vary:
Vary the cosine similarity threshold and record the most salient sentence.
Does the most salient sentence change as you vary the threshold?
- the cosine similarity threshold determines how similar two sentences have to be in order to share and edge.
- the salience threshold determines how high a sentence's PageRank has to be in order for that sentence to be included in the summary.
- Accordingly, report on a cosine similarity threshold that gave you the best result (if applicable).
- Compare the 1 sentence summary to the 2 or 3-sentence summary.
In your opinion, how much do the 2nd and 3rd sentences add (in terms of adding more information).
- Would you have chosen them, or a different sentence?
Relate your answer to the structure of the lexical similarity graph.
Submission of your homework is via WebCampus.
You must submit all the required files in a single pdf document containing all the answers.
Acknowledgement: The assignment is modified from Lada Adamic.