# CS 765 Complex Networks

## Due on Thursday Oct 27, 2016 at 2:30 pm

Random graphs and giant components (2 points)
1. Go to http://ccl.northwestern.edu/netlogo/models/GiantComponent and launch the applet. Click 'setup' and then 'go'.

2. 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.
Growing networks: preferential and random growth (3 points)

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.

1. 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?
2. 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?
The Watts Strogatz small world model (2 points)

Go to http://ccl.northwestern.edu/netlogo/models/SmallWorlds. This is a NetLogo model that will allow you to vary the rewiring probability.

1. 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?
2. Try using a spring layout. In what ways do the random links make the world smaller?
LexRank (3 points)

Select a piece of text (10-20 sentences) that you would like to summarize and paste it in the appropriate box of the LexRank demo.

If you are unable to paste text into the text box, try a different browser.

1. There are two parameters you can vary:
• 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.
Vary the cosine similarity threshold and record the most salient sentence. Does the most salient sentence change as you vary the threshold?
2. Accordingly, report on a cosine similarity threshold that gave you the best result (if applicable).
3. 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).
4. Would you have chosen them, or a different sentence? Relate your answer to the structure of the lexical similarity graph.